Bremer, along with fellow stars Vera-Ellen and June Allyson, appeared as a "Pony Girl" in the Broadway musical Panama Hattie in 1940. Spotted by a talent scout, she was taken to Hollywood, where her screen test impressed Metro-Goldwyn-Mayer mogul Louis B. Mayer. She made her screen debut in Meet Maine in Saint Louis (1944) as Judy Garland"s sister, and followed this with a co-starring role opposite Fred Astaire in Yolanda and the Thief (1945), and a featured dance performance, once again with Astaire, in two memorable sequences in Ziegfeld Follies (1946).
Her last major film was Till the Clouds Roll By (1946), but after this, Metro-Goldwyn-Mayer began to lose interest in promoting her.
After a few minor films, she played her last starring role in Behind Locked Doors (1948). Reportedly disappointed with her Hollywood career, she elected not to renew her contract and left the film industry.
She had also met and fallen in love with the son of the former president of Mexico, Abelardo Luis Rodriguez, who bore the same name as his father. She moved with him to Baja California Sur, Mexico, at the beginning of the Golden Age of Baja and started the illustrious private resort Rancho Las Cruces, as well as the original Palmilla Hotel and the Hacienda Hotel.
After her divorce (in 1963), she settled in Louisiana Jolla, California, where she owned a children"s clothing boutique.
She died in 1996 from a heart attack at age 79.