CHARLESTON, S.C. -- At almost the same moment that the White House was announcing a Washington summit between President Reagan and Soviet leader Mikhail Gorbachev, Vice President Bush perched cross-legged on a high stool here Friday and told 150 South Carolina supporters that "I don't know what my role will be" in the most dramatic meeting of the Reagan years.

"I'd like to take part," he told a questioner, "but I've got to continue to do what I need to do every day . . . to win this nomination." A few minutes later, he added to a television reporter, "I'm just going to put my head down and keep working."

Meet the new George Bush, the self-appointed Tortoise of Republican politics, a far cry from the man who made "I've got Big Mo" (momentum) the battle cry of his 1980 presidential campaign.

These last few days were arguably the best politically for Bush since March 1980, when his hopes for the presidency effectively ended in the New Hampshire primary defeat that snapped the "Big Mo" he had gained by upsetting Reagan in the Iowa caucuses.

Last week, the stock market slide, which jeopardized public confidence in the economic policies of the Reagan-Bush administration, halted -- at least for now. The U.S.-Soviet summit, seemingly scuttled a week ago by Gorbachev's intransigence, was scheduled for early December, ensuring that the intermediate-range nuclear missile treaty that Bush alone among the Republican contenders has championed will be signed before the primaries begin.

And on Wednesday in Houston, Bush emerged from the first GOP candidates' debate as the unexpected but unanimously recognized winner -- a high hurdle for a candidate who had never fared well in such a forum.

Bush could have been forgiven for grinning or gloating -- as he did in his "Big Mo" days -- but instead, the face he presented to the world was that of the sober-sided, earnest striver.

"I'm not going to get caught up in wins and losses," he told a handful of reporters aboard Air Force Two the morning after the Houston debate. "I'm just going on to the next event."

The next events for Bush were not high-profile public appearances. He talked space policy, education and economics to audiences in Alabama, Mississippi and here, generating useful local publicity. But the backbone of his schedule since Houston has been closed-door fund-raisers and organization meetings with supporters in the "Super Tuesday" southern primary states.

"I know how I got to be vice president," Bush said at the organizational meeting here. "It takes lots of hard work in the precincts."

Despite Wednesday's debate success, the Bush organization is relying far more on its organizational and financial muscle than on any hope that Bush will consistently outshine his five opponents on the television screen. "There are six more televised debates before Super Tuesday," a campaign strategist explained, "and it's virtually impossible for him to do as well in all of them as he did in Houston. So why set up a debate win as the be-all and end-all?"

Rather than count on Bush coming up with the big play whenever it's needed, his managers intend to grind out victory by steadily strengthening his front-runner status and forcing the other contenders to gamble. In the Bush strategists' view, former secretary of state Alexander M. Haig Jr. and former Delaware governor Pierre S. (Pete) du Pont IV -- the long shots in the GOP field -- gambled and lost by taking on Bush in the Houston debate.

The next time out, they guess, it may be Rep. Jack Kemp (N.Y.) or television evangelist Marion G. (Pat) Robertson who feels pressure to go for Bush's jugular.

Eventually, the rival they most fear, Senate Minority Leader Robert J. Dole (Kan.), will have to give up the "Mr. Nice Guy" role he fashioned for himself in Houston, they think, and try to bring down Bush.

Bush is preparing for that moment in four ways. He is trying to learn the counterpunching tactics he conspicuously lacked during his brief period as front-runner in 1980. He was ready for Haig's and du Pont's criticisms in Houston, and his rebuttals were effective. "I know I'll take a lot more shots," he told reporters Thursday, "and if they get too cheap, I'll hit right back."

The second goal is to improve the consistency of his day-to-day speaking and news conferences, seeking to avoid the verbal gaffes that marred the end of his recent European trip and his candidacy announcement swing. "He has to show he can sustain it, not blow it every third day," one strategist said.

The third goal is to capitalize on his main advantage over his rivals, his seven-year-old alliance with Reagan. Bush would like to reach the point at which any attack on the vice president will be seen as an act of irreverence toward the Republicans' icon, Reagan. The test audience whose reactions to the Houston debate were measured scientifically by the Bush campaign gave its strongest approval to his refusal to utter a word of criticism of Reagan. The positive scores soared when Bush said, "In my family, loyalty is not considered a character defect, it is considered a strength."

Finally, Bush hopes to be stronger on the ground -- especially in the Super Tuesday southern states -- than anyone else. The Charleston stop was the first of six this weekend in South Carolina, an intensive organizing drive that will take him into each of the state's six congressional districts. With many key endorsements in hand and the prospect of public support soon from Gov. Carroll A. Campbell Jr. (R), Bush hopes to show his strength in the South Carolina primary on Saturday, March 5 -- three days before the Super Tuesday voting in the rest of the South and elsewhere.

"This state can be the weather vane," Bush told his supporters here. "If you do what I think you can do, this nominating process can be over on March 8."