Bain was born Mildred Fogel in Chicago, the daughter of Russian Jewish immigrants. She graduated from the University of Illinois with a bachelor's degree in sociology. Developing an interest in dance, she moved to New York City, where she studied alongside Martha Graham. Dissatisfied with her career as a dancer, she went into modeling; jobs with Vogue, Harper's, and other publications followed.
Still uninspired, however, Bain entered the Theater Studio to study acting, first under Curt Conway, then Lonny Chapman. Progressing to the Actors Studio, she was instructed by Lee Strasberg.
Bain's first acting role was in Paddy Chayevsky's play Middle of the Night, which embarked on a national tour in October 1957. Accompanying Bain was fellow actor and new husband Martin Landau; the final leg of the tour brought the couple to Los Angeles, where they settled permanently. After moving, Bain established herself at the Actors Studio West, where she continued to teach classes and perform scene work.
Bain's earliest television appearances included CBS's Tightrope, with Mike Connors, and three ABC series: The Law and Mr. Jones with James Whitmore, Adventures in Paradise with Gardner McKay, and Straightaway with Brian Kelly and John Ashley. After a recurring role as David Janssen's romantic interest in Richard Diamond, Private Detective in 1959, she guest-starred as Madelyn Terry in a 1960 episode of Perry Mason, "The Case of the Wary Wildcatter", and in 1964 played the role of Elayna Scott in "The Case of the Nautical Knot".
In 1965, she guest-starred alongside series star Jerry Van Dyke in an episode of My Mother The Car, which also featured Avery Schreiber's recurring role of Captain Bernard Manzini. She also appeared in the 1966 final episode of the series alongside Van Dyke.
Between 1966 and 1969, Bain appeared—alongside her then-husband, Martin Landau—in the major role of Cinnamon Carter in Mission: Impossible; she also starred as the character in a 1997 episode of Diagnosis: Murder. She won three consecutive Emmy Awards for Best Dramatic Actress for her performance in 1967, 1968, and 1969, in addition to a Golden Globe Award nomination in 1968.
She starred opposite Landau again in the science-fiction TV series Space: 1999 (1975–77), as Dr. Helena Russell, and the made-for-TV film The Harlem Globetrotters on Gilligan's Island (1981). Bain also appeared in The Dick Van Dyke Show, in the episode "Will You Two Be My Wife?", and My So-Called Life, playing the main character Angela Chase's grandmother in one episode. Other appearances include "Matryoshka", an episode of the 1990s science-fiction series Millennium.
In 1998, Bain appeared in the Walker, Texas Ranger episode "Saving Grace", as the mother superior. In 2006, she had a minor role in one episode of CSI: Crime Scene Investigation ("Living Legends"). In 2008, co-starring with her daughter Juliet Landau, Bain voiced the character of Verdona Tennyson in "What Are Little Girls Made Of?", an episode of Ben 10: Alien Force.
On April 28, 2016, Bain was honored with the 2,579th star on the Hollywood Walk of Fame, located at 6767 Hollywood Blvd. Lifelong friends Edward Asner and Dick Van Dyke were on hand to speak and assist in the unveiling of the star.
Bain married actor Martin Landau in 1957; they divorced in 1993. The couple have two daughters, actress Juliet Landau and film producer Susan Bain Landau Finch (born Susan Meredith Landau). Bain is Jewish. She has contributed to many charitable causes, including literacy. Bain suffers somewhat from claustrophobia, which the writers of Mission: Impossible incorporated into her character on the show in the episode The Exchange.