As a stand-in for President Reagan without presidential powers, Vice President Bush is attempting to keep a low public profile while being neither brash nor timid in the top-level meetings over which he now is presiding.

And it was easy to keep that low profile yesterday. Reagan had planned to spend the day in Springfield, Ill., addressing the state legislature, so there were no presidential events which Bush had to add to his schedule. He went through an unremarkable series of appointments including a lunch with CIA Director William J. Casey and a meeting with former Irish Foreign Minister Garret Fitzgerald, the leader of the opposition Fine Gael Party.

An earlier vice president, Richard M. Nixon, described becoming a stand-in as one of his six crises. After President Eisenhower had a heart attack Sept. 24, 1955, Nixon wrote later in his book "Six Crises" that he realized, "Every word, every action of mine would be more important now than anything I had ever said or done before because of their effect upon the people of the United States, our allies and our potential enemies."

"My problem, what I had to do, was to provide leadership without appearing to lead," Nixon wrote, noting that it would be dangerous for him to make any move that might be interpreted as an attempt to usurp the powers of the presidency.

Bush aims to achieving the same balance, according to White House sources, but he is having a far easier time than Nixon.

For one thing, Bush is generally trusted by the Reagan inner circle. Most important, White House Chief of Staff James A. Baker III was Bush's 1980 campaign manager before joining the Reagan-Bush campaign. In addition, presidential counselor Edwin Meese III was one who advocated early on that Reagan should choose Bush as his running mate.

"Bush is performing extremely well. He's filling in for the president without being brash or overly assertive. I speak for everybody here," Baker said yesterday.

As a symbol of his role while Reagan remains hospitalized, Bush presided at his first Cabinet meeting Tuesday sitting in his usual chair and leaving Reagan's chair vacant.

However, Bush has not been so deferential as to be reluctant to take charge when needed, one White House aide said. At the Cabinet meeting he reportedly broke in on the discussion at a couple of points to call for additional staff work.

Bush also canceled all his travel plans through the end of next week to remain in Washington for at least the early days of Reagan's recovery. U.N. Ambassador Jeane J. Kirkpatrick will substitute for Bush at a Geneva conference on African refugees, White House deputy press secretary Larry Speakes announced.

Nixon reported that "I did my best during this period to avoid meeting the press," and Bush seems eager to follow that example. In normal times the vice president moves around alone without the group of reporters that always trails after the president. Bush decided to keep it that way.

The vice president allowed reporters to see him only once yesterday at a brief session in the Roosevelt room during which he said he is not used to such intense interest from the media.

When reporters at the White House requested Bush to describe his Tuesday visit to Reagan in the hospital for cameras, he chose to do it in a formal setting with the visiting prime minister of the Netherlands instead of making his statement in the White House press room where reporters would undoubtedly have attempted to ask him questions.

"What the vice president wants to do is conduct his schedule in a normal fashion and assume what is necessary of the president's responsibilities while keeping very close to the senior White House staff," Peter Teeley, Bush's press secretary, said.

Bush had been sitting in on almost every major meeting the first two months of the Reagan administration so the absence of the president has not meant a drastic change in his schedule. In contrast to yesterday, however, today will be busy. It will include the regular Thursday Cabinet meeting, a session with Republican members of the House Ways and Means Committee who are vital to the chances of passage of Reagan's tax package and a meeting with Poland's deputy prime minister Mieczyslaw Jagielski.