In a "Dear Friend" letter to thousands of voters in his massive district, Congressman Robert Bauman has vowed he will "not go back to the personal hell I had created" and asked for understanding and "one more chance" on election day.

The three-term incumbent, fighting for political survival after his own admission to the "twin compulsions" of alcoholism and "homomosexal tendencies," also appeared in television commercials on local stations, telling constituents; "I've worked hard to be an effective congressman even when my personal problems were the most difficult."

In keeping with the tone he set at an emotional press conference five days after he appeared in D.C. Superior Court and agreed to undergo rehabilitation rather than face trial on a charge that he had solicited sex with a 16-year-old youth, Bauman is again going to the public to admit the error of his ways and seek understanding.

It is common political strategy employed by candidates beset by disclosure of personal or legal problems.

Two years ago, New York City Congressman Frederick C. Richmond, facing a charge that he had solicited sex from an undercover policeman in Washington, immediately sent an open letter to his Brooklyn constituents admitting that he had also tiried to buy sex from a teen-aged youth in his home. He suggested in the letter that the solicitations resulted from being under "intense pressure." He apologized "from the bottom of my heart for any hurt I may have caused" and asked for "compassion and understanding at this extremely difficult time for myself, my parents, my son, my staff and for you."

Five months later, Richmond won a dogfight of a Democratic primary against three challengers in his liberal district, where even spiritual leaders had shrugged off the morals charge.

The 43-year-old Bauman, running in the conservative and deeply religious district on the Eastern Shore that runs from the Pennsylvania to the Virginia border, is having a harder time, with polls showing him trailing his Democratic challenger, State Del. Roy Dyson, by as much as 21 percentage points.

Bauman sent out the "Dear Friend" letter, dated Oct. 24, to the district's nearly 250,000 voters, according to a state Republican Party official.

In it, Bauman told citizens they deserved "a full explanation," and went on to recount that in the last two years he had turned "increasingly to the use of alcohol following the daily sessions in Congress. Although I did not drink during working hours and public events, my late-night drinking became more and more uncontrollable.

"But alcoholism is no excuse," the three-page letter went on. "In addition to my alcoholism, I have also suffered from other personal problems, of which you have no doubt read. Last winter during the period of my worst drinking, these personal problems worsened as well.

"I knew what I was doing was wrong."

Bauman, never identifying in the letter what his other problems were, said they were threatening to "destroy my marriage." He talked in the letter of seeking and receiving help, and of putting his problems in the past. Then, recounting his efforts to fight inflation, hold down government spending and work for a strong national defense, Bauman asked voters to give him "one more chance when you vote Nov. 4."

Similarly, in campaign commercials running on Eastern Shore stations, Bauman, seated on a Chippendale-style couch with his wife, Carol, beside him, mentions his "personal probems," talks of his record and concludes: "There's so much more I can accomplish but first I need your vote Nov. 4."

On Wednesday, Bauman received the editorial endorsement of his hometown newspaper, the Easton Star-Democrat, while the largest newspaper in his district, the Salisbury Times, which had supported him in the past, endorsed Dyson.