Republican Robert E. Bauman, asserting that his problems with alcoholism and homosexuality "are over and done with," announced today that he will seek to regain the congressional seat he lost last year following public disclosure of his troubled personal life.

A slimmer, calmer, but still feisty Bauman stood in the same ornate room at the Tidewater Inn where he had watched his promising political career dissolve in a narrow defeat last November. He attempted to take the offensive against incumbent Roy Dyson, the Democrat who beat him, but still faced numerous questions about his personal life at the wide-ranging press conference.

"For almost two years now, I have faced the realities of my own personal existence, and I have been given the rare opportunity afforded to few of us in our lives to address my inadequacies and set wrongs aright," Bauman said. "And that I have done."

Today's announcement merely confirmed what most in the sprawling First Congressional District had known for months -- that Bauman is eager to regain the seat he lost last November after disclosure that he had agreed to undergo court-ordered rehabilitation rather than face trial on a charge of soliciting sex with a teen-aged boy.

"His life is Congress," said Maryland Republican Party chairman Allan Levey. "Despite everything, he wants to be back there. He knows how difficult it will be. In fact, if it wasn't for that difficulty, he'd be the incumbent."

Before the revelations last October, Bauman, the acknowledged parliamentary wizard and verbal sharpshooter of the Republican right, had a lock on the seat he had held for nearly a decade in this conservative district. Dyson, a one-time Maryland state delegate who pursued the House seat for years, has been looking over his shoulder nervously for months at a possible comeback by the still-popular Bauman.

The two have been conducting a war of opposing pollsters. Last summer, Bauman announced results of a poll showing him beating Dyson in a hypothetical rematch. The poll, conducted in May, showed about 42 percent of those surveyed supporting Bauman and about 34 percent supporting Dyson, if the election were held at that time.

Dyson has since countered with two polls of his own -- the latest released last Sunday, on the eve of Bauman's formal announcement and the day Bauman held a party for about 150 supporters at the Tidewater Inn. Dyson's poll, conducted last month, showed 56 percent of those questioned would vote for Dyson against 29 percent for Bauman.

Today at Bauman's press conference, the battle of percentages escalated.

"The liberal incumbent from this district voted against President Reagan's economic program seven out of ten times on key votes," Bauman charged, saying he had gotten the list of anti-administration votes from the White House congressional liaison office. "And all the while he has professed that he wanted to give the president what he termed a chance. Well, I want to help the president."

From his Capitol Hill office, Dyson responded by reading a letter from President Reagan thanking him for support on the administration's tax-cut bill. "I don't know what Bauman is talking about," Dyson said. "Somebody is wrong here, and I would not question the White House."

Bauman also charged that Dyson has "misled" his constituents, by telling them that he "is a budget-balancer and a conservative."

Dyson refused to be drawn into debate. "I'm not going to respond to every jot and tittle that Bob Bauman has to say. I'm a United States congressman," said Dyson. "I've focused my attention on the constitutional crisis we faced this weekend . . . not worrying and responding to all his questions."

Dyson aide Tony Pappas added that "there is no way" Dyson would accept Bauman's challenge to debate in the District's 13 counties because Bauman "has not even gotten his party nomination yet."

Former Maryland state senator C.A. Porter Hopkins may seek the Republican nomination, according to some party officials on the Eastern Shore, but he has not yet announced his intentions.

Bauman's prospects are likely to hinge on whether his former constituents focus on his political record or his personal life, said one party official.

But Bauman today was predicting victory, exhibiting the same self-assurance that has won him both admirers and enemies. "I have repeatedly been told about the need for the return of the watchdog of Congress," he said, referring to his self-styled role in the House. "I was a damn good congressman," Bauman said later. "If I was good then, having met my problems and solved them, I think I'll be a better person and better congressman, too."