The public learned something about George Bush last week that he had hoped to keep secret for awhile: The vice president has become an influential insider in Ronald Reagan's administration.

The day after President Reagan had faced down an angry Secretary of State Alexander M. Haig Jr. and formally confirmed his choice of Bush as the administration's crisis manager, Bush sat in his White House office and said:

"What happened yesterday, with my name cropping up there, is an embarrassment to me. I'm not competing for something.I want to do what the president wants me to do and I want to do it well . . . but I'm not seeking assignments. I'm not saying, 'Let me do this or that.'"

Despite the disclaimer, an examination of Bush's activities over a 10-day period climaxing with the announcement of his role as the president's stand-in on domestic and foreign policy emergencies left no doubt that he is playing an increasing role in both the domestic and national security operations of this administration.

It was a span of days in which Bush:

Announced the first substantive steps in the administration's drive to cut back cumbersome government regulations.

Delivered federal financial help to Atlanta's child-murder task force and offered his sympathies to the bereaved families.

Defended Reagan programs in nine speeches to audiences as sympathetic as wealthy Florida Republicans and as skeptical as black publishers.

Huddled twice with Republican senators to plot strategy on the Reagan budget.

Conferred with government officials from Japan, West Germany and Argentina, leaders of the Republican National Committee, the American Jewish Committee, the North Carolina legislature, the Conservative Political Action Conference, the Asia Foundation, the Associated Builders and Contractors and the Business-Higher Education Forum, among others.

Still managed to spend about three hours a day with the president.

"I go home tired at night," Bush said, "but I have a good job and I want to be effective at it."

It was at Reagan's 70th birthday party that the president leaned over to Barbara Bush and said, "I want to ask you a very personal question. Is George happy with his job? Does he feel what he's doing is worthwhile? I just want to be sure he's doing enough. If the awful-awful should happen, George should know everything."

That is not how it began. Reagan and Bush had known each other for 16 years, but the relationship had never been close and, at times, it verged on being antagonistic.

Bush had bristled when Reagan went to Texas in 1978 to campaign for a Republican opposing Bush's son for a coveted congressional nomination. Reagan and his aides thought Bush was still and sappy in last year's Nashua, N.H., primary debate and unnecessarily savage in his Pennsylvania primary assult on Reagan's "voodoo economics."

Reagan balked at pressure from his asvisers to pick Bush as his running-mate and acquiesced only when the draft-Jerry Ford boom appeared to be turning into a midnight horror show at the Detroit national convention. James A. Baker III, then Bush's campaign manager and now Reagan's chief of staff, says, "Everyone knows the president didn't want to pick Bush. . . . There was absolutely no understanding between them of what Bush's role would be."

Bush confirms that as a fact and says, "I never yet have sat down with him and defined all this. It has just evolved."

In an interview Friday with The Washington Post, Reagan said that "while we didn't have an opportunity to get down into details," he said always wanted Bush "as closely involved in the administration as . . . possible . . . . It's working very well."

There is, as Bush acknowledges, a precedent in the partnership between Jimmy Carter and Walter F. Mondale over the previous four years. Mondale was the first vice president to be granted a genuine working role in an administration.

Anxious to see his breakthrough institutionalized by his successor, Mondale and members of his staff were (in the words of Chase Untermeyer, the former Houston legislator who is Bush's executive assistant) "extraordinarily helpful" to Bush and his aides during the transition period.

Bush inherited the perquisites that signaled Mondale's unique status: the West Wing office, just down the corridor from the Oval Office; access to presidential briefing papers; integration of key vice presidential staff members into the functions and meetings of the presidential staff; a private, weekly luncheon for the president and vice president -- alone.

To some members of Bush's staff who had worked for previous Republican vice presidents, these status symbols seem almost like miracles. Thaddeus Garrett Jr., Bush's domestic policy adviser, had served as a junior staff member to Nelson A. Rockefeller. "Rockefeller was here -- and only here," Garrett said, indicating the Executive Office Building suite across from the White House. "He was not made privy to the meetings and briefings of the president."

Victor Gold, Bush's part-time speechwriter and political consultant, was Spiro T. Agnew's press secretary. "When I was with Agnew," Gold recalled, "I never had a White House pass. I didn't get into the White House more than five times in the 30 months I worked here. When Agnew made a speech, we flew in a plane with no windows. That's where we stood."

By every account, Bush's role has grown in proportion to Reagan's confidence in his loyalty and ability -- and the personal warmth that has melted previous suspicions. A close friend of Nancy Reagan says, "She and Barbara and the president and George have really become devoted to each other."

Edwin Meese III, counselor to the president, says the relationship was forged during the fall campaign."Every report on George was positive," he recalls. "He's a good team player."

On the Bush side, the stress on loyalty reflects the lingering concern about acceptance by the Reaganites. Press secretary Peter Teeley -- whose anti-Reagan barbs during the primaries made him the target of an abortive purge effort by some Reagan aides when Bush went on the ticket -- says of his boss: "He fully recognizes that the president is the president and his role is to be supportive. He was absolutely no hang-up about that either."

Rich Bond, the architect of Bush's upset of Reagan in the Iowa caucuses and now his deputy chief of staff, says, "Bush would not tolerate my being on his staff if I weren't prepared to work fully and cooperatively with Reagan and his staff. "I'd be gone tomorrow if George thought I was spending one second on anything but making this administration a success. He's made it very clear that if we don't like that arrangement, we should go work some place else."

A Republican senator, according to a colleague who was in the room, had been lecturing his audience of GOP committee chairmen about the rotten, insensitive, ungrateful way Reagan's patronage dispensers had treated old supporters when it came to filing White House staff jobs. Bush, who was a guest at the session, decided he had heard enough.

"Aside from being elected president yourself," he said to the senator, "just how damn much do you think you ought to have to say about who is working there?"

The vice president's only constitutionally prescribed duty is presiding over the Senate, and Bush has been as skimpy in the time alloted to that function as his predecessors were. Unlike them, however, he has been invited into the inner caucuses of the Senate.

Old-timers on Capitol Hill recall that when former Senate majority leader Lyndon B. Johnson became vice president, he sought to preside -- as had been his prerogative -- at the Senate Democratic caucus. Politely but firmly, Johnson was told that it was a meeting of senators.

While the vice president is an officer of the legislative branch, he is an agent of the president. Mondale, a Senate alumnus, observed the Johnson precedent by visiting Senate Democratic policy meetings only rarely.

But Bush -- the son of a former senator -- was invited by Majority Leader Howard H. Baker Jr. (Tenn.) and Republican Policy Committee chairman John G. Tower (Tex.) to sit in on the weekly meetings of Republican committee chairmen in Baker's office and the policy lunches of all GOP senators that follow them.

"I'm there through the courtesy of Baker and Tower," said Bush, who sits between the two Senate leaders at the lunches. "Its useful, because people can come up to me and say, "Tell the president you can't do this, or you ought to do that.' They let off steam on personnel problems and other things, and I get a pretty good sense of the mood that I can share with him."

Bush's offices in the Capitol and a Senate office building are headed by Susan Alvarado, who was the first woman to serve as a floor assistant to the Senate leadership when she worked for Republican Whip Ted Stevens (Alaska), and Robert Thompson, an Oklahome businessman and party leader without previous Hill experience.

Like Bush, they disclaim the role of White House lobbyists. But Thompson attends the daily morning meetings of Reagan's congressional liaison staff and he and Alvarado function continually as pipelines of information from the Capitol to the White House.

They also schedule Bush for the variety of small favors that build good will for an administration in Congress: taping a television program for two Mississippi congressmen or the two Pennsylvania senators; meeting constituents of a Florida congressman. In keeping with current White House policy of courting Democratic support for Reagan's program, Bush dispenses these favors on a bipartisan basis.

He entertained Democratic and Republican senators Saturday at a brunch at the vice president's house, and is going to Chicago this week to address a Polish-American dinner at the request of Dan Rostenkowski (D-Ill.), chairman of the House Ways and Means Committee.

But when the Baker and House Republican leader Bob Michel (Ill.) dropped by Bush's office Tuesday morning, it was a strategy session on the Reagan budget -- one of three such meetings for Bush last week. "He's close to us because he was a House member himself," Michel said, "and we like to get him into our sessions."

Bush says he needs to spend more time with his former House colleagues -- in part because success for the Reagan program is far less assured there. "I get up to play paddle-ball with the guys in the House gym on Saturday mornings," he said, "but that's pure R-and-R. I had Conable [Rep. Barber Conable of New York] in here talking about ways I can be more useful in the House fights ahead, without making a pest of myself."

Bush's working day normally begins at 7:40 a.m. in the spacious formal office in the Executive Office Building. His appointments secretary, Jennifer Fitzgerald, who worked with him in the liaison office in Peking and when he was director of the Central Intelligency Agency, builds his schedule around the president's.

"That is my first priority," Bush says, "because you've got to establish a relationship, build it and strenghten it. You've got to know enough about what he [the president] is exposed to so you can give useful advice."

The schedule for last week showed Bush sitting in on all of Reagan's meetings with members of Congress and foreign leaders. Often, the schedule was arranged so Bush could see the foreign visitor -- Japanese Foreign Minister Masayoshi Ito, for example -- in the White House Roosevelt Room just before they joined the president in the Oval Office.

"He's very good at describing the president to them," says Nancy Bearg Dyke, the former Senate aide and deputy assistant secretary of the Air Force who is Bush's national security adviser. "He tries to make sure they understand Reagan's economic program and view of the world before they go in to see him."

In the last week, Bush also participated with Reagan in meetings of the auto import task force, the Cabinet council on economic affairs and other ad hoc meetings on topics that Bush and his aides declined to specify.

Baker, Meese and Michael K. Deaver, Reagan's third top side, pop into Bush's West Wing office half-a-dozen to a dozen times a day, according to Fitzgerald and Untermeyer, who share the space with him.

While Bush's biggest specific assignment before the crisis management job was to head the task force on regulatory reform, it has not consumed a great deal of his time. Staff work has been handed to C. Boyden Gray, Bush's counsel and a newcomer to his staff.

While Bush took a one-hour briefing before conducting the news conference where the first set of specific regulatory targets was unveiled, Gray says Bush prefers to work on the regulatory assignment at home on weekends rather than let it cut into his regular weekday schedule.

He is similarly detached from the tax-and-spending portions of the Reagan economic plan. Bush says he attends meetings on these subjects "only for information purposes so I can better articulate the program to the public or to a congressional group. I'm not trying to direct or guide anything."

What does strongly engage his interest is national security policy -- not surprising in view of Bush's service at CIA, in China and at the United Nations. His chief of staff, retired admiral Daniel J. Murphy, was Bush's CIA deputy and after years of experience in major military commands served as deputy undersecretary of defense.

On a typical morning, Murphy and Dyke meet at 7:30 to go through the same CIA briefing book the president receives, and 45 minutes later -- while Murphy is sitting across the table from Baker at the White House senior staff meeting -- Dyke gives Bush his first national security briefing of the day. Two hours later, Bush and Murphy join Reagan and his national security affairs adviser, Richard V. Allen, to go over much of the same material, and Bush and Murphy also are in the National Security Council meetings.

When he was vice president, Mondale remarked of his suite in the Executive Office Building: "When you're over there, you might as well be in Baltimore." But throughout his career, Bush has had close working and personal relations with his staff -- and he has continued that despite the problems of working in a White House office where only four other people can find desk space.

Each morning at 8:50, when Murphy returns from the White House senior staff meeting. Bush meets his own senior staff in the EOB office for a planning session. Increasingly, he has scheduled his own meetings with outside visitors for that same suite, rather than his White House office.

"I think when I bring interesting people over there, just by osmosis it makes my staff feel a part of things more," he says. "And I don't feel threatened by being away from the White House a few hours. I don't feel that anyone is trying to get me. . . . So I don't feel I have to wait on the edge of my chair for someone to come in and clue me in on something."

"Bush's Ignorance Insulting to Florida," the headline on the Miami News editorial said, and the comment on the vice president's statements on the four-day swing in mid-March were acid: "The harbinger of new beginnings admitted to his embarrassment that he did not know what the Carter administration promises to Miami for post-riot aid included, exactly, and he didn't know what the Reagan administration planned to do about those promises either. . . . In Naples, last weekend, he admitted . . . that he did not know anything about Florida being denied federal aid this winter after the freeze damaged citrus crops. He also did not know about the progress, relatively speaking, of interstate highway construction in Florida." p

The traditional role of vice presidents has been that of traveling salesmen for their presidents. Bush has not avoided that, but neither has he sought to expand it -- as some distant predecessors did -- in hopes of building his own political base. With Reagan putting a moratorium on his own political travel, the demands on Bush are heavy. Bush had a working lunch with Republican National Committee officials last Monday to seek guidance on the criteria he should use in deciding which to accept.

The Florida trip was originally scheduled for the launch of the first space shuttle, and when that was postponed, the Bush staff scrambled to find other events to fill his calendar. The trip showed signs of improvisation -- and also of his rustiness as a campaigner. Without the knowledge of Rich Bond, his top political aide, Bush accepted the suggestion of a couple Florida Republican officials and publicly endorsed, in his Naples speech, a 1982 ticket of Rep. L. A. (Skip) Befalis for governor and Rep. C. W (Bill) Young for senator.

Only afterward did he learn that there were other aspirants for those nominations in the room at that party fund-raiser and they were less than pleased with his speech.

As for the items that the Miami News criticized him for ducking, Bush says, "I knew both sides of those issues, but the Florida congressmen said, 'Don't get involved . . . avoid it.' So I deliberately didn't answer. . . . I've got to seek a better balance between saying 'I don't know' and butting into every local issue."

Back in Washington, Bush took his support of the Reagan policies before two sharply contrasting groups in a single day: the Conservative Political Action Conference in the morning and the National Newspaper Publishers Association at lunch.

To the conservatives, many of whom have been skeptical of Bush's conservative credentials, he stressed that the "conservative mandate" of the 1980 election will not be "deterred or detoured . . . by the liberal advocates of the status quo."

"He has learned a lot from Reagan," one conservative activist remarked approvingly.

To the black publishers, Bush repeated his statement that the election was a rejection of the status quo, but he insisted that "the president's critics are woefully off-base when they charge that this administration has gone after existing social programs with a meat ax." In that audience, there was open skepticism -- and some criticism of the absence of a question-and-answer period.

But Bush says he will continue to take the case for the Reagan program to critical constituencies, noting that in recent weeks he has met in his office with AFL-CIO President Lane Kirkland, NAACP Executive Secretary Benjamin Hooks Jr. and National Urban League President Vernon Jordan. "I want to make myself accessible to them," he says.

It had been a tumultuous 10 days -- from the emotional visit to the families of the Atlanta victims and those seeking the killers to the fight over Haig's objections to Bush's assignment from the president as crisis manager.

Bush went to extraordinary lengths to avoid grandstanding on the Atlanta trip, discouraging Georgia senators and representatives from accompanying him, and barring any direct photo or press coverage of his meetings. At the other end of the time span, he reemphasized his normal, low-profile approach by issuing orders to his staff to avoid comment on the Haig flap.

Yet, as Bush continues his public advocacy of the Reagan program and takes on additional assignments for the president, attention and controversy are sure to grow -- and so is the question where it is leading him in 1984 or 1988.

Bush is aware of the danger -- and powerless to prevent it. "If I'm another player in the field, protecting my turf and bragging about how close in I am, that inevitably strains things," he said in an interview. "That's exactly why I've never wanted to talk to anybody [in the press] about the way my job is developing.

"I'm convinced that people will write the 'Whatever happened to George Bush?' story, and then that's good . . . because if I'm out there high-profile, trying to grab credit . . . that would quickly undermine whatever utility I have to the president."

If he really believes that, Bush must have loved the article that greeted him in the Miami Herald when he arrived in that city on the same day as Andrew Young. The item in the local gossip column read: "George Bush, another former U.N. ambassador, who is rumored to have a job in the Reagan administration, speaks at 11:30 today at the Omni. . . ."