Bromley began her career in the 1930s on contract with Monogram Pictures, she was first billed as Sheila LeGay starring in 1930 westerns alongside Tom Tyler. She frequently co-starred with Ken Maynard, Hoot Gibson, Johnny Mack Brown, Bill Cody, and Dick Foran. She first starred alongside Bill Cody in the 1932 western Land of Wanted Men. She starred opposite John Wayne in the 1935 films Westward Ho & Lawless Range and the 1937 film Idol of the Crowds. In 1944 Bromley appeared in the touring production of Good Night Ladies. In 1960 she appeared as a central character Mrs. Spencer alongside Paul Brinegars character Wishbone in the Rawhide episode "Incident of the Deserter". She appeared in one episode of I Love Lucy as Helen Erickson Kaiser, the childhood friend of Lucy Ricardo. She also made five guest appearances on Perry Mason during the series' nine-year run on CBS. In her first appearance in 1959 she played co-defendant Agnes Nulty in The Case of the Borrowed Brunette. In 1962 she played murderer Elizabeth Dow in The Case of the Mystified Miner.

During World War II she worked often for the USO, continuing that Service until the war ended in 1945. There she met her husband Jairus Bellamy. She is credited with seventy-five films in her career, of which seventeen were westerns, for which she is best known. Bromley retired from films and lived in the Greater Los Angeles Area until her death in 2003.

On July 23, 2003, Bromley died in Los Angeles, California. The reference work Obituaries in the Performing Arts, 2003 gave her age as 95.