Crosby began acting at age four in a stage production of "Peter Pan", which starred her mother. As a child, she did TV commercials for Minute Man orange juice with her parents and brothers, and also appeared on Bing Crosby's variety specials, notably those aired at Christmas. After attending the University of Texas, to which she was admitted at age 15, Crosby began her career in earnest. In 1979, she was the dream girl on the short-lived series "Brothers and Sisters" (NBC), and also appeared in episodes of the "Dallas" spin-off "Knots Landing" (CBS, 1980). After leaving "Dallas", she did guest appearances and appeared in TV longforms. After the national attention she received in 1981, Crosby parlayed the fame into the leading role of a woman stalked in the remake of the Doris Day thriller "Midnight Lace" (NBC, 1981). She was a sexually voracious insider in ABC the miniseries "Hollywood Wives" (1985). But by the late 80s, her career had cooled somewhat, although she often appeared in independent features and direct-to-video releases like "Quicker Than the Eye" (1988) and "Deadly Innocents" (1989). "Eating" (1990), an ensemble piece by Henry Jaglom, played art-houses, but Crosby never really found a star-making big screen vehicle.

Crosby turned to the stage and won critical applause for her work as Juliet in an L.A. production of "Romeo and Juliet" (1988) and more recently reunited with Larry Hagman as a guest ion his short-lived comeback series "Orleans" (CBS, 1997).