Vice President Bush, declaring victory here tonight amid cries of "Bush in '88," urged his supporters to come together with Democrats and seek "the universal goal of peace, prosperity and opportunity for all."

"In this wonderful hour of victory," Bush told a crowd of Texas Republicans in his adopted home town, "let us not forget that the strength of our free system lies not only in the right of the majority to express its will, but in the right of all Americans to have their voices heard and their interests served."

The crowd of 1,000, waving placards such as "Fry Fritz and Ferraro," and "Kick Ass George," booed Bush's mention of Rep. Geraldine A. Ferraro (D-N.Y.). But the unity-minded vice president reproved them. "No, she campaigned very, very hard. She was a strong opponent," he said. "Let's come together as one people."

The crowd cheered boisterously earlier when President Reagan declared victory, and issued his first thank-you to Bush "for campaigning so magnificently all across this country."

"George, if you're watching down there in Texas," Reagan said to Bush via television, "I'm proud to have you for my partner this next term. As far as I'm concerned, there has never been a finer vice president."

Earlier in the evening, when the landslide was taking shape, Bush attributed it to the popularity of Reagan's vision of America.

"The president got his message out. I think Mr. Mondale got his out, I guess," Bush said as he watched the returns in a 23rd-floor suite of the Westin Galleria Hotel.

The buoyant windup for Bush was in contrast to a campaign that a close adviser called "the most difficult race he has ever had to run."

"In the final days, Bush occasionally lost his sunny demeanor, calling the campaign "tough," "grueling" and "just plain ugly."

At the end of his last stump speech here Monday night, a call for unity and prosperity at a welcome-home rally, he flung his arms apart as if he were a runner crossing a finish line and declared: "The campaign is over . . . Last stop! I can hardly believe it!"

In ways it was only the beginning. Bush, 60, is widely acknowledged as the front-runner for the Republican presidential nomination in 1988. Throughout the campaign Bush was under scrutiny not only as the understudy to President Reagan but also as a presidential contender-in-waiting.

Bush's speech here tonight was interrupted by cries of "Bush in '88," as were others during his travels to 97 cities since Labor Day. One of his aides yesterday displayed a button bearing Bush's picture and the slogan "12 more years" -- presumably four with Reagan, eight on his own.

"Too early to even consider it," was all that Bush would say when reporters asked about his 1988 plans as he emerged from the voting booth today.

Further spotlighting the normally low-profile task of running as vice president was that Bush's counterpart, Ferraro, was making history as the first woman candidate for the post on a major party ticket.

There was feverish speculation early in the campaign, even within the GOP, about whether Bush could "handle" a debate with Ferraro. "It got to me," Bush said last week. Polls showed that voters believe that he soundly defeated her in their televised encounter.

Bush thought so too. In perhaps his most memorable words of the campaign, he crowed to a longshoreman in Elizabeth, N.J., the morning after the debate, that "We tried to kick a little ass last night."

The remark became his unofficial rallying cry, with supporters greeting him from then on at campaign stops with placards and buttons declaring "Kick Ass George," and his aides speculating that it will be one of his 1988 slogans.

While Bush had intended to stay out of the headlines and simply to extol the Reagan vision of peace through strength and prosperity ("I don't like to make news," he said. "I don't like to be flamboyant"), Ferraro capitalized on her historic role to court news coverage and heavily overshadowed him.

Still, polls showed that voters believed that Bush was more prepared than Ferraro to assume the presidency in an emergency, and his favorable ratings of 60 percent in most surveys easily bested hers.

What made the campaign tough for Bush, according to his closest advisers, was that it brought him his toughest treatment ever by opinion-makers, from conservative columnists George F. Will and William Safire to what Bush called the "liberal bastions" of the national media.

As Reagan's self-described cheerleader, Bush portrayed the president as a force for peace and pilloried Democrats for their charges that he had made the world more dangerous. To Walter F. Mondale's charge that Reagan was unfair to the poor, Bush hailed the economic recovery as a tonic that healed all Americans.

Bush spent most of Election Day secluded here in his adopted home town with his wife, Barbara, and three of his four sons. He ventured into the public only to vote and to play an inning of baseball with his staff and the national press.

A former Yale baseball team captain and first baseman, Bush fielded one out at first after taunting batters: "I dare you push one down here." To staffers' cheers, he later scored a run, reaching first base on an error and home on a triple.

"This has been the most difficult race he Bush has ever had to run," said adviser Vic Gold. "Here's a person who has always had favorable press. And this time, I think he was targeted by the media as well as the Democratic opposition. He took the blows, and in some cases the shafts intended for Reagan."

"This has been a big transition for him," Gold said. "He had been set up as a preppy who wears striped watchbands and minds his manners, but anybody who's listened to George Bush over the years knows he's a true conservative and that kick-ass is well within his vocabulary. Now everybody knows it."