Born in Flushing, New York, Bessell grew up in Manhasset on Long Island, New York. He was originally gearing up for a career as a classical musician. As a 12-year-old child prodigy, he performed a piano recital at Carnegie Hall. Bessell played lacrosse in high school with future football star and actor Jim Brown. However, after graduating from college in 1958, Bessell focused on acting. He studied with Sanford Meisner at the Neighborhood Playhouse, studied dance and dramatic movement with Martha Graham and Louis Horst, was a member of a professional acting class under Meisner, and worked with Wynn Handman in another professional acting group. Bessell also worked at ABC New York as a Page (Usher) to supplement his income in the late 50s. TV shows he appeared in included ‘Who Do You Trust?’ with Johnny Carson and ‘the Dick Clark Show,’ a Saturday night variety show featuring rock ‘n roll stars. He directed and acted in stock where he appeared in a wide spectrum of theatre works ranging from Shakespeare to Jule Styne. He then was cast in the off-Broadway production of The Power of Darkness, which led to further off-Broadway work with the Blackfriars Guild. He also co-produced with his brother, writer-director Frank Bessell, Joe Orton’s Crimes of Passion, directed by Michael Kahn. Bessell first went to Los Angeles in the West Coast production of Thomas Wolfe’s Look Homeward, Angel, for which he received great critical notices. Following that he appeared in the film The Outsider with Tony Curtis and in Lover Come Back with Rock Hudson and Doris Day as an elevator operator. In 1962, Bessell played 27-year-old college student Tom-Tom DeWitt on the short-lived NBC comedy/drama television series It’s a Man’s World with co-stars Glenn Corbett, Michael Burns, and Randy Boone. In 1965 he appeared as Corporal Smith in second season episode 3, “Then Came The Mighty Hunter” of 12 O’Clock High. In 1966, he was regularly featured on Jim Nabors’s Gomer Pyle, U.S.M.C. as Private Francis Lombardi, one of Gomer’s fellow Marines. Bessell also appeared in feature films like McHale’s Navy Joins The Air Force and Don’t Drink the Water with Jackie Gleason and Estelle Parsons. He also appeared in the TV film, Your Money Or Your Wife, which won the Peabody Award for Best Mystery of the Year.

Bessell’s best-known TV role was as Donald Hollinger, Marlo Thomas’ boyfriend and fiance on the hit series That Girl, which ran for five seasons from 1966 to 1971. (In the first pilot, he was Donald Blue Sky, who had a trace of American Indian ancestry. In addition to being the boyfriend, he was also her agent.) When that series ended its run, Bessell tried his hand at another sitcom, Me and the Chimp, created by Garry K. Marshall, which had a short, unsuccessful run in 1972. It was not until 1975 that he would appear in another sitcom, in the character of Joe Warner, the boyfriend of Mary Richards for two episodes on The Mary Tyler Moore Show. In the 1980s, Bessell appeared in several TV movies, including Breaking Up Is Hard to Do and The Acorn People. He also played regular roles on a pair of unusual sitcoms, Good Time Harry and, in his last major role, Hail to the Chief, as the husband of Patty Duke’s character, the first female President of the United States. Neither of these series was successful. Bessell moved into directing, helming episodes of The Tracey Ullman Show and Sibs. In 1989, he shared an Emmy as a producer on Fox Broadcasting’s Tracey Ullman, which was honored as best variety or comedy program. Bessell died on October 6, 1996 due to an aortic aneurysm. He was preparing to direct the big screen version of the TV series Bewitched. He is interred in Woodlawn Cemetery in Santa Monica, California.