At about 8 p.m. Dec. 12, Vice President Bush received calls from the White House situation room and the State Department, alerting him that the Polish government had imposed martial law and had ordered a crackdown on the Solidarity movement.

A few minutes later he called President Reagan at Camp David and broke the news. Then Bush headed to the White House to take command of the "special situation group" monitoring the Polish crisis.

Throughout the day last Sunday the group -- including top officials of the State and Defense departments, the National Security Council and the White House staff -- conferred in the situation room and by telephone. At 4:30 p.m., when Reagan returned to the White House, Bush led the briefing group that discussed the dramatic developments with the president.

That pattern continued for most of the week as the Reagan administration dealt with its biggest foreign policy challenge through a mechanism led by the vice president.

When that fact was publicized by the White House, it caused another in a series of recalculations about the role and standing of George Bush, a seeming resurgence of influence for a man who has more than once been dismissed as a fringe player in the administration.

In his first year on the job Bush has experienced at least his full quota of the usual vice presidential ups and downs. Shunted into the sideline area of regulatory reform during the rush to launch the administration's tax and budget cuts, he was thrust to the forefront by his calm, circumspect performance during the anxious hours and days after Reagan was shot.

For a time, the cameras followed Bush wherever he went, but as the president recovered Bush once again stepped into the background.

Something like that seems to have happened in the Polish situation. When the news reached Washington last weekend, presidential counselor Edwin Meese III and Secretary of State Alexander M. Haig Jr. were thousands of miles away. National security adviser Richard V. Allen was on administrative leave and under Justice Department investigation.

By all accounts, Bush performed well under pressure last week, as he had done when he came flying back from Texas to a shaken White House hours after Reagan was shot March 30.

But when Meese and Haig got back to Washington last week, "crisis manager" Bush absented himself for 40 hours, from Thursday afternoon until yesterday morning, to keep some routine fund-raising and speech-making commitments for the Republican Party and the administration in New Mexico and California.

If Bush finds his off-and-on utility infielder role at all aggravating he does not allow it to show.

"I don't feel a sense of great frustration in the job," he said in a mid-week interview. "It's been a very happy experience."

The key, Bush said, "has been the development of a good confidential relationship with the president . . . in an environment where I feel perfectly free to discuss controversial things with him and give him my honest opinion and best judgment."

How useful or influential those opinions and judgments are to the government of the United States probably can be judged by only one man, President Reagan, and he is not talking. A suggestion from Bush's press secretary that Reagan be interviewed this week by a small group of reporters doing stories on Bush was turned down by the president's staff.

Without that testimony the evidence is inevitably somewhat mixed and inconclusive.

For example, when administration insiders talk about the power structure in the White House, Bush is almost never described as being in the same league as "the Big Three": Meese, James A. Baker III and Michael K. Deaver.

The skepticism about his influence is buttressed by the fact that, since Labor Day, Bush has spent 47 of 104 days on the road, part of a hectic travel schedule that took him to 31 states and nine foreign countries this year.

But on Capitol Hill, Republican leadership aides aver that "Bush is around when we need him more than any other recent vice president." And his standing with the president was demonstrated, not only by his role in the Polish crisis, but by the White House decision last week to designate Richard N. Bond, Bush's top political aide, for the sensitive job of deputy chairman of the Republican National Committee in charge of 1982 campaign plans and operations.

Former vice president Walter F. Mondale, whose "insider" role in the Carter administration set the standard by which Bush is judged, has suggested in more than one recent interview that Bush lacks the access and influence that Mondale enjoyed.

But a Bush associate said, with some heat, "You find me a time when Mondale was running the crisis-management operations. You show me when Carter ever let a Mondale staff guy take charge of the whole Democratic campaign. Then I'll admit that Bush is a lesser light."

There are such great differences in the top personalities and the operating methods of the two administrations that it is probably futile to attempt a comparison. But Bush is sensitive to it. Shortly after he had Mondale in for a social lunch, The New York Times reported that, "Unlike Mr. Mondale, Mr. Bush is not included in the 'paper loop' of option papers and memorandums that senior White House staff members send to the president."

Bush had an aide query the presidential staff on the matter, and the reply, detailing a dozen categories of memos and briefings that go to the president and vice president simultaneously, is now given routinely to any reporter who inquires about Bush's status in the "paper loop."

Bush said his relationships with "the top staff and the president himself have been excellent. I don't feel threatened" when excluded from the insiders' decision-making.

Like Mondale before him (and no other vice president), Bush has an office in the West Wing of the White House, just down the corridor from the president's, and an invitation to sit in on any Oval Office meeting. Aides say he has been increasingly willing to "walk in" on the president.

Reagan and Bush have a private luncheon almost every week, following another Carter-Mondale innovation, and it is at those sessions, Bush says, that he offers most of his opinions and advice.

"There has not been one leak from those lunches," Bush said with some satisfaction, "and developing that relationship of trust with a man I respect, I'd say, has been the major thing I've accomplished this year."

It must be in those private sessions that Bush has his say, for Cabinet members and White House staff members are unanimous in saying that Bush is conspicuous only by his silence at the meetings they attend with the president.

When Bush was asked about the reported "reticence" or "reluctance" on his part, he said, "It's a lot more than that. It is an absolute determination not to express myself. Suppose several Cabinet members, or even one Cabinet member, expresses a view, and I express a contrary view. I don't think the president should ever have to choose between me and a Cabinet member. That's not the way to have a relationship of confidence.

"And suppose I express one view and the president expresses a contrary one. I don't think the president and vice president should ever be publicly in opposition. Incidentally," he added, "Mondale agrees very strongly with that."

Mondale said that he had offered that advice to Bush at a meeting shortly after the election, but had added that there had been, of course, times when his strong feelings on a subject had prompted him to speak out in a Cabinet meeting. So far as anyone can recall, Bush has not done that.

Instead, he has maintained a busy schedule of activities, ranging from $3 million worth of fund-raising dinners and receptions for the Republican Party to meetings with 130 foreign dignitaries. He serves as a listening post for the White House on Capitol Hill, meeting almost every week with Republican Senate committee chairmen and playing paddle ball with old House pals in the House gym.

He has been a good-will ambassador to constituencies that feel little good will toward the administration, holding more meetings with labor and black leaders than any other senior official has.

Along the way, he has made a few publicized gaffes: an overly effusive toast to Philippine President Ferdinand Marcos, which seemed to embrace his regime as a model of democracy, and a disclosure of President Anwar Sadat's death that preceded and preempted the official announcement from the Egyptian government.

But around the White House Bush is praised as a team player who, in the eyes of his colleagues, has done nothing that is seriously embarrassing and much that is at least marginally helpful to the president's successes.

For knowledgeable politicians the strongest proof of Bush's good standing was the appointment of Bond as deputy chairman of the RNC last week.

Bond ran the Bush campaign in the Iowa caucuses, and helped give Bush the victory that almost derailed Reagan's nomination drive before it was fairly started.

Bond's new job is one of the most coveted in American politics: running the mid-term campaign. It is the job that Hamilton Jordan had at the Democratic National Committee in 1974 and that Charles Black had at the Republican National Committee in 1978. And it is no accident that the candidates for whom they worked in the subsequent nomination battle, Carter and Reagan, prevailed.

Any astute political operator -- and Bond is one -- in that job will bring away the most intimate, detailed knowledge of the strengths and weaknesses of the campaign organizers in the 50 states and the 435 congressional districts where presidential nominations are fought and won.

Bush's critics in the conservative movement understand what Bond's job could mean to Bush in any battle for the 1984 nomination, and they have been vocal in condemning the appointment.

But to Bush's friends, who would like to see him succeed Reagan in 1985 or 1989, the Bond appointment is proof positive that Reagan is neither dissatisfied nor disappointed with his vice president.

And that is the way George Bush mightily wants to keep it.