Wives: Adrienne Marden (23 November 1938 – 1954) (divorced), two children. Dilys Mary Shan Jukes (5 December 1954 – 11 January 1958) (her death), one child. Jennifer Raine (24 November 1967 – 5 January 1993) (her death).

In a career that began with the film Holy Matrimony (1943), Bissell appeared in hundreds of films and television episodes as a prominent character actor. Regularly cast in low-budget science fiction and horror films, his roles include a mad scientist in the film I Was a Teenage Werewolf (1957) and Professor Frankenstein in I Was a Teenage Frankenstein (also 1957).

Bissell appeared as a guest star in many television drama series between the early 1950s and the mid-1970s, with more sporadic appearances after that. He guest-starred in a couple of episodes of The Lone Ranger. He appeared on other syndicated series, including Sheriff of Cochise, Whirlybirds, Peyton Place and The Brothers Brannagan. He was cast in the religion series Crossroads and Going My Way, and in the NBC education drama series Mr. Novak.

He played the attending Psychiatrist who treats the protagonist, Dr. Miles Bennell, played by Kevin McCarthy, in Invasion of the Body Snatchers (1956) and appeared in Creature from the Black Lagoon (1954).

Bissell played murderer Larry Sands on CBS's Perry Mason ("The Case of the Crooked Candle", 1957). He made three other Perry Mason appearances, including the role of Max Pompey in "The Case of the Lavender Lipstick" (1960), and Laurence Barlow in "The Case of the Nautical Knot" (1964). He appeared in an episode of Peter Gunn. (1958) He played different roles in multiple episodes of the ABC series The Rifleman.

From 1959-61, Bissell was a regular for the third and fourth seasons of the television series Bachelor Father, costarring John Forsythe, Noreen Corcoran, and Sammee Tong. He was cast three times on the long-running NBC western series The Virginian.

In 1960, Bissell had appeared in George Pal's production of The Time Machine, as Walter Kemp, one of the Time Traveller's dining friends. He also appeared in a 1978 TV movie adapting the H. G. Wells novel for a more modern setting. Bissell's Time Tunnel co-star, John Zaremba, also appeared in the telemovie. Thirty-three years later, in 1993 the documentary film Time Machine: The Journey Back (which featured Bissell, Rod Taylor and Alan Young), Bissell recreated his 1960 role as Walter in the opening sequence. It was Bissell's last acting performance.

Bissell's most prominent television role came when he played as General Heywood Kirk in 30 episodes in the 1966–1967 season of the science-fiction television series The Time Tunnel. He often played silver-haired figures of authority, here as in many other roles (as described by AllMovie), "instantly establishing his standard screen characterization of fussy officiousness", leavened in many instances with a military bearing. Other examples of such authoritative roles as military or police officials, include appearances in The Caine Mutiny, The Manchurian Candidate, The Outer Limits (1963), Hogan's Heroes (1966), and The Man from U.N.C.L.E. (1966).

In 1978 and 1980, Bissell appeared in episodes of The Incredible Hulk, first in the second-season episode "Kindred Spirits", and next (and lastly) in the second part of the fourth season two-parter "Prometheus". He played a different professor in both episodes.

Bissell received a life career award from the Academy of Science Fiction, Fantasy and Horror Films in 1994. He also served for many years on the board of Directors of the Screen Actors Guild, and represented the actors' branch of the Academy of Motion Picture Arts and Sciences board of governors.

Bissell died in 1996 at the Motion Picture & Television Country House and Hospital in Woodland Hills, California from the effects of Parkinson's disease. He was interred in the Westwood Village Memorial Park Cemetery in Los Angeles.