Vice President Bush, who was in Texas yesterday to give two speeches on President Reagan's economic program, flew quickly back to Washington last night and quietly took charge of the crisis at the White House as the nationa awaited news of the president's condition.

About 8:30 p.m., once it became clear that Reagan had pulled through surgery successfully, Bush made a short statement, expressing great pleasure that the president had survived with "flying colors," and reassuring the country that the "American government is functioning fully and effectively."

Characteristically, Bush made no reference to his own role, a sharp contrast to the performance earlier in the day of Secretary Alexander M. Haig Jr., who had asserted in a televised news conference that he was "in control" while Bush was away. Later, Bush said through his press secretary, Peter Teeley, "The president is still in charge. There has been no mechanism put in place to transfer authority."

Bush's plane landed about 6:30 p.m. at Andrews Air Force Base, where a helicopter was waiting to rush him to the city. However, rather than land on the White House South Lawn, a prerogative normally reserved for presidents, Bush chose to alight at the Naval Observatory, where he was met by presidential counselor Edwin Meese III, and traveled by motorcade to the White House.

There he met in the situation room with Meese, chief of staff James A. Baker III, Haig, Defense Secretary Caspar W. Weinberger, Attorney General William French Smith and others.

Bush declined to answer questions after his press statement, and press spokesman Larry Speakes refused to discuss the content of the meeting.

Bush learned of the assassination attempt as he was airborn between Fort Worth, where he had addressed a cattle raisers' convention, and Austin, where he was to speak to a joint session of the Texas legislature. The session was canceled, and a prayer session was to be held instead.

Teeley said he telephoned, Bush aboard Air Force Two at 2:40 p.m. and told him that shots had been fired at the president but that, according to initial reports, Reagan was not hurt. About a half-hour later Bush learned that the president had, in fact, been wounded, Teeley said.

Security at Andrews Air Force base last night was extra tight, with armed agents squatting on top of the hangar where Bush disembarked. House Majority Leader Jim Wright (D-Tex), who had accompanied Bush on the trip, said the vice president had displayed "total calm with complete control of his emotions" throughout the ordeal.

Bush's reaction to the news of the shooting, Wright said, was "one of shock and disbelief." The vice president sounded as if he could not comprehend "that anyone could work up a feeling of sufficient malice for President Reagan to want him dead," Wright said.

Wright said the trip back to Washington was a very "somber flight because of the warm and tender feelings many of those on board have for Jim Brady," Reagan's press secretary, and because of concern over the president's condition.

He said that during the flight, those on board exchanged stories about other presidential assassinations. And at one point, he said, someone recounted the reaction of Harry Truman to Franklin D. Roosevelt's death. Vice President Truman reportedly said to the late Speaker of the House Sam Rayburn, "Sam, I can't do it." Rayburn replied, "Yes, you can. You have to. . . ."

Texas Secretary of State George Strake, who met with Bush aboard Air Force Two as it stopped to refuel in Austin, said the vice president "looks like he's in total control of himself." He added that Bush was in a "state of dismay on how it takes a single individual to pass a bad reflection on the whole United States."

Texas Gov. Bill Clements and his wife, Rita, also boarded the plane to speak to Bush.

Bush's Texas swing, which was to be followed by an address this week to a Polish-American dinner in Chicago, is part of a hard-driving campaign he has undertaken to sell Reagan's economic program to the nation. In nine speeches during the last few weeks, Bush has taken the lead in pushing the package around the country, while Reagan has stayed close to Washington. Bush has also taken an active role in working with congressional leaders to pass the package in the House and Senate.

If he should have to assume the reins of government, Bush, who is next in the line of succession to the president, would appear to be a man prepared for the job. Since the election, he has been an integral part of Reagan's inner circle.

Although Bush was Reagan's keen rival during the Republican priamry and was Reagan's reluctant choice as a running mate, he has been a loyal ally and the relationship between the two men has become personally close over the last few months. Bush occupies a West Wing office just down from the president's, enjoys access to presidential briefing papers, has his staff integrated into the workings of the presidential staff and eats lunch once a week alone with Reagan.

Most recently, Bush, a former ambassador and director of the Central Intelligence Agency who has a strong interest in foreign policy, was named the administration's crisis manager, a position coveted by Haig.

Bush was a logical man to sell the president's program in Texas yesterday, because, although he was born in Massachusetts and raised in Connecticut, he made his fortune in the oil fields of West Texas. Together with some friends, he formed the Zapata Petroleum Co., which found profitable oil wells around Midland, Tex., and then the Zapata Offshore Co., which became a pioneer in seabed drilling equipment.

Bush, whose father, Preston, was a senator from Connecticut, was elected to Congress from Houston in 1966 and served two terms in the House, where he voted as a conservative on fiscal matters and defended big oil. Defeated by Lloyd Bentsen in a race for the Senate, Bush was nevertheless rewarded with the job of ambassador to the United Nations. In 1972, when Richard M. Nixon was looking for someone both loyal and honest to take the job of Republican National Committee chairman, he went to Bush.

Bush traveled tirelessly throughout the next year, making 113 speeches in 40 states and trying to purge the taint of Watergate from the party. In the process, he cemented political alliances with Republican officials across the country, a move that would serve him well when he undertook a lonely battle for the presidency six years later.

On October 1974, President Ford named Bush his envoy to Peking, where he remained about a year before returning to Washington to head the CIA.

In 1976, Bush was unemployed. But he had watched carefully and learned a lesson from Jimmy Carter's primary campaign. By 1977, he was running for president, a two-year grass-roots effort that followed the Carter model all the way to the winning of the Iowa precinct caucuses. But in the battle for the nomination that followed, Bush, although he was in most ways as conservative as Reagan, was unable to withstand the Reagan onslaught.

Reagan chose him as his running mate only when the draft-Jerry Ford effort fizzled and the presidential nominee's advisers heavily pressured him to balance the ticket with someone who could appeal to moderate, East Coast Republicans.

Throughout his career, beginning perhaps with his captaincy of the Yale baseball team, Bush has been known as a "team player." Whether in defending Nixon against Watergate or in selling Reagan's economic ideas -- which he had labeled "voodoo economics" during his primary campaign -- Bush has proved repeatedly to be a man of remarkable political flexibility.

"I want to do what the president wants me to do and I want to do it well," he told The Washington Post in an interview last week.

The loyalty was apparently mutual. During Reagan's 70th birthday party, the president leaned over to Bush's wife, Barbara, 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."