On the second day of George Bush's official quest for the presidency last week, the thrill of his announcement was temporarily squelched by a freezing shower in a New Hampshire motel. It was out of hot water.

In a nearby room a campaign aide discovered her first gray hair.

Then things got worse.

At a Concord, N.H., press conference, Bush was drawn tarbaby-like into a vague foreign policy question. The more answer he gave, the more question he got. "If we're going to maul him," one Washington reporter said to another, "let's sit up in the [TV] lights."

"I learned a lot from that," Bush said later of that low point in his first campaign week.

"It was a minor glitch," his campaign manager James A. Baker, added.

Indeed it was. For by the end of the week, in George Bush's first days as a declared candidate for president, he had demonstrated an ability to attract key people and draw money to his candidacy.

In New Hampshire, he had announced that former campaign managers for Ronald Reagan and Gerald Ford were now on his side. At a morning breakfast in Florida he nailed down the support of a well-respected former state legislator and paid for his leased DC9 campaign plane with a Miami breakfast that raised $15,000. And in Alabama he announced that George Wallace's top campaign aides from 1972 and 1976 were now behind George Bush, mailing lists and all.

Not bad for someone who admits he doesn't "even show up in the polls."

There he was, 54 and running for president, the newest of the Republican candidates for the job but not an unexpected candidate. George Herbert Walker Bush, considered three times for the vice presidency by Richard Nixon and Gerald Ford, has spent more than a year jockeying for a run at the Big Job.

He normally announced last Tuesday at the National Press Club. He trails in the public opinion polls but takes comfort in his standing as many people's "second choice." After all, in 1974, when Gerald Ford needed to appoint a new vice president, Bush was the second choice of the likes of both Barry Goldwater and Nelson Rockefeller.

Bush will point out that he is not everybody's second choice; that there are a goodly number of respected Republicans who see him as their first choice. And that, he and his campaign manager agree, "ain't no bad place to be," as Jim Baker puts it.

It means, according to the Bush strategy, that if he can get off to good start in the early primaries and precinct caucuses of 1980,those who had supported other candidates who drop out early will gather under his candidacy.

He is candidate for the first time since 1970, when he lost a U.S. senate race in Texas. By last Thursday he became so wound up in a speech to 425 Florida Republicans that after reciting a long list of American ills he blurted, "...then what the fff... [pause] in heaven's name is going to happen to our country?"

The next night in Clanton, Ala., speaking at a $6-a-plate county Republican fund-raiser, he was given a series of tokens by the Possum Growers and Breeders of America Inc. that included a membership card, a certificate of appreciation and a license plate reading, "Eat more possum."

Then to the surprise of all, the mayor of Clanton thrust at George Bush a baby possum, which Bush dangled by the tail for all to laugh at.

He did it with a certain horrified grace.

What people do to be president.

On thing Bush is not doing is worrying for now about his name recognition-not until, he says, it becomes a problem in raising money or winning key supporters. CAPTION: Picture, GEORGE BUSH . . . "I learned a lot"