Vice President Bush raced through a busy day yesterday during which he assumed many of the functions and ceremonial duties, but not the powers, of the presidency.

The vice president arrived at the White House at 7:40 a.m. to begin his first hectic day as stand-in for President Reagan while Reagan recovers from the gunshot wound he suffered in Monday's assassination attempt. r

Real power and decision-making authority, officials made clear, remained with the wounded president in a hospital room less than a mile from the White House. But many of the public duties and obligations that accompany power fell to Bush as he crisscrossed the city from the White House to the hospital to Capitol Hill, all the while attempting to project an image of "normalcy" and business as usual.

Bush's schedule yesterday, as it is likely to be in the days ahead, was a combination of some of his own obligations and those that previously had been scheduled for the president. He began the day, as Reagan normally would, by meeting with the three top presidential advisers, Edwin Meese III, James A. Baker III and Michael K. Deaver.

At noon, Bush fulfilled another presidential obligation by hosting a working lunch for Prime Minister Andreas van Agt of the Netherlands. But later in the day, the vice president also met with Transportation Secretary Drew Lewis in his regular role as head of an administration task force on government regulation, then traveled to Capitol Hill to preside in the Senate during the closing debate and vote on a budget amendment opposed by the administration.

"He's in a very good mood," Bush's press secretary, Peter Teeley, said near the end of the day. "He feels good about the president."

The first event that departed from what would have been the normal schedule at the White House yesterday came at 9 a.m., when the vice president presided at a Cabinet meeting. The previously unscheduled meeting was called, according to Teeley, to inform the full Cabinet of the exact situation regarding Reagan's condition and the functioning of the government in the wake of the shooting.

At 10 yesterday morning the president had been scheduled to meet with Republican congressional leaders. In his place, Bush met with an expanded congressional group that included Democratic leaders who also were given the latest information on the situation.

Later in the morning Bush traveled to George Washington University Hospital for a five-minute visit with Reagan. While at the hospital, he also briefly visited wounded White House press secretary James Brady, Brady's wife, Sarah, and Timothy J. McCathy, the Secret Service agent who also was wounded in the shooting.

A short time later, arriving at the Capitol, Bush told reporters that Reagan had been awakened when he visited him in the hospital room.

"The president, to me, looked well and was very responsive [and] asked with his unfailing courtesy about Barbara, my wife," he said. "Mrs. Reagan was there."

Bush's morning visit to the Capitol -- the first of two he made yesterday -- was his most concerted effort to show a business-as-usual attitude as the day's events unfolded. Normally, the vice president attends a Republican policy lunch on Capitol Hill on Tuesdays. Yesterday there was no time for the lunch, but Bush thought it important to make an appearance in Congress.

At 11:20 a.m., he casually strolled onto the Senate floor and spent about 10 minutes quietly chatting with small groups of the dozen or more senators who then were on the floor.

"The vice president wanted to come by to show a sense of normalcy, say hello to a few people and then leave," said Sen. Slade Gorton (R-Wash.).

From the Senate, Bush was whisked back to the White House to greet van Agt. At the end of the working lunch, both Bush and van Agt reaffirmed Dutch-U.S. ties in a ceremony that took place in brilliant sunlight outside the diplomatic entrance to the White House. Van Agt said he and his coutrymen were "shocked by the events of yesterday [Monday]," and wished the president "a speedy and full recovery."

Late yesterday, after leaving Capitol Hill for a second time in the day, Bush traveled to the Washington Hospital Center to visit Thomas K. Delahanty, the D.C. police officer who also was wounded in the shooting outside the Washington Hilton Hotel.

Aides indicated yesterday that there is a desire to keep Bush in Washington, at least for a while, and that most of Reagan's scheduled out-of-town appearances will be canceled rather than have Bush travel in his place.

The first trip to be canceled was Reagan's scheduled appearance today before a joint session of the Illinois legislature in Springfield. White House officials said they also expect to cancel a trip to Cincinnati April 8 for the opening of the major league baseball season.

Bush yesterday showed every indication of relishing the extra duties that came to him. His only complaint, voiced to reporters at the Capitol, was that after all the chaos of Monday he ended up eating peperoni pizza and a milk shake and as a result, "didn't sleep too well."