Vice President Bush, making his first public appearance since President Reagan was shot on Monday, campaigned at Tysons Corner last night in behalf of Virginia Attorney General J. Marshall Coleman, the likely Republican candidate for governor.

The vice president's appearance at a campaign rally in suburban Northern Virginia served the dual purpose of demonstrating the normalization of activities following the assassination attempt and emphasizing the Reagan administration's commitment to the election of Republican Coleman in Virginia this year. He declared that this year's gubernatorial election will be a test of Reagan's program.

Security was described by one of the 500 persons who paid $50 each to attend the reception as "incredibly tight." Secret Service agents cleared the ballroom of the West Park Hotel in the midst of the two-hour rally to make sure it was safe before Bush's arrival at 6:40 p.m.

Outside the hotel, uniformed officers from Fairfax County, D.C., the National Park Service and plainclothes agents leading police dogs surveyed the parking lot and kitchen entrance to the hotel and stopped reporters at the door to scrutinize their credentials.

But no one complained about the precautions. When Bush arrived, he gave the crowd an up-to-date report on the president's condition, saying that when he visited the president at George Washington University hospital a few hours earlier Reagan was "sitting up, signing papers, keeping things going and just doing great." The crowd cheered when Bush said that "it's so important to the free world that he have a speedy recovery."

Bush also reported that he had "peeked in" on press secretary James Brady and that while he was doing "remarkable . . . he has a long way to go."

In his 12 minute talk, Bush said that the Virginia election is "a national highlight, one of two tests that year on how the Reagan program is going." The other is the gubernatorial election in New Jersey.

Coleman is anxious to make his campaign a referendum on the Reagan program too. He told the partisan gathering that "I don't think of this as an isolated campaign."

"Until the tragedy," Coleman said, "I am not sure the American people understood what a jewel" of a president the nation has. When Reagan "was wheeled into the hospital and said, 'I hope you are Republicans,' he did more for our party. . ."

Gov. John N. Dalton, who introduced Bush, said the vice president is the first of four key Reagan administration spokesmen who will appear at Coleman rallies this month: Budget Director David Stockman will go to Richmond, Treasury Secretary Donald Regan to Roanoke and special trade representative Bill Brock to Norfolk.

In each instance, Dalton said, the Reagan administration representatives said, "Tell me when to be there. I want to help."

While Coleman is tying his campaign to Reagan, he also is seeking to tie his opponent, Lt. Gov. Charles S. Robb to former president Jimmy Carter and his Democratic predecessors, including Robb's late father-in-law, former president Lyndon B. Johnson.

Dalton, who views Coleman as his protege, said that voters who think there is "no difference" between Coleman and Robb "should know where these two men were the Sunday night before the election" last November. Coleman was with him, Dalton said, campaigning for the Reagan-Bush ticket, while Robb was "across town trying to elect Jimmy Carter. And in 1984, Ronald Reagan is going to be elected again, and we want a governor in office who will be backing him, not fighting him."

Bush, picking up on Coleman's campaign slogan, said he was "delighted to do my part to 'keep a good thing going.'" He said he had "known Marshall Coleman for some time, and found him to be an able legislator, a remarkable attorney general who is going to be a fantastic governor."

The vice president said he had read Coleman's platform and found it "sounded very much like what we are trying to do at the federal level, by offering regulatory relief, tax relief and spending cuts."