The son of Walter Bergman, a United States Navy officer, he was born in Guantanamo Bay, Cuba. He later graduated from Crossland Senior High School in Camp Springs, Maryland. Bergman was married to actress Christine Ebersole from 1976 to 1981. In 1985, he married Mariellen, with whom he has two children.

In a Vicks Formula 44 cough syrup advertising campaign in 1986, Bergman told the viewing audience, “I’m not a doctor, but I play one on TV.” Chris Robinson, who played Dr. Rick Webber on ABC’s General Hospital, was the original spokesperson in the ad campaign, which started in 1984. Bergman replaced Robinson after the latter experienced some legal difficulties. The writer of the commercial used this opening line as a disclaimer, because the then-existing “white coat rule” prohibited people from portraying doctors in commercials without some sort of clarification/disclaimer. The original commercial with Chris Robinson became the most-recalled TV commercial in the history of the Vicks brand.

Since 1989, Bergman has played the role of Jack Abbott on The Young and the Restless. In 1997, Bergman portrayed Jack Abbott in an episode “The Heather Biblow story” on The Nanny, where he shared an on-screen kiss with Pamela Anderson. In 2001, he guest starred as Jack on The King of Queens in an episode of Season 3.