Bruce was born Shirley Levy in Great Neck, New York to Beatrice and Harry Levy. She had a sister, Marilyn.
Because of her family's moving, she attended Jamaica High School, Girls' High School, and New Utrecht High School before graduating from Erasmus Hall High School in Brooklyn, New York. Although she studied violin for eight years, she never took singing lessons.
Bruce began her career as a singer in the late 1930s with Larry Clinton and his band. She sang with Ben Bernie's orchestra in 1940-1941.
Bruce made her Broadway debut in Louisiana Purchase, with songs by Irving Berlin, who discovered her at a nightclub in Newark, New Jersey. She was the first actress to play the role of Julie in a Broadway production of Jerome Kern and Oscar Hammerstein II's Show Boat since the 1932 Broadway revival. Bruce played the role onstage in 1946 and garnered favorable comparisons to Helen Morgan, who had originated the role onstage in 1927 and repeated it in both the 1932 revival and the 1936 film.
Her other Broadway credits include New Priorities of 1943, Along Fifth Avenue, Do I Hear a Waltz?, Henry, Sweet Henry, and A Family Affair.
Bruce appeared with Abbott and Costello in Keep 'Em Flying (1941). Her first serious film role was in This Woman Is Mine (1941). She had supporting roles many years later in the films American Gigolo (1980) and Planes, Trains and Automobiles (1987).
Bruce's radio debut came on The Horn and Hardart Children's Hour. She sang on Carton of Pleasure and The Henny Youngman Show.
After a long career as a singer and in films, Bruce is probably best-remembered for her recurring role as the domineering and meddlesome "Mama Carlson" (mother of the station manager played by Gordon Jump) on CBS' WKRP in Cincinnati. Sylvia Sidney played Mr. Carlson's mother in the pilot episode.
Bruce's only marriage (to Milton Nathanson, which ended in divorce) produced a daughter, Julie, an actress, singer and playwright who married jazz guitarist Larry Coryell. Bruce's grandchildren, Murali and Julian Coryell, are both musicians.
Bruce died from chronic obstructive pulmonary disease at the Motion Picture & Television Country House and Hospital in Woodland Hills, California, aged 87. She was also survived by her sister and two great-grandsons.