Born in Englewood, New Jersey, Birch began her career as a dancer in Broadway musicals, including Brigadoon, Goldilocks, and West Side Story (playing "Anybodys"). She has directed and choreographed music videos for Cyndi Lauper, the Rolling Stones, and Carly Simon.
She earned Emmy Awards for her direction of the television specials Natalie Cole: Unforgettable and Celebrating Gershwin and, in collaboration with Michael Tilson Thomas, she staged the concert version of On the Town performed by both the London Symphony Orchestra and the San Francisco Symphony. She spent six years staging numbers for Saturday Night Live. In the 1960s, she taught dance at the Juilliard School's pre-college division in New York City. She has performed as a soloist with Martha Graham and Agnes de Mille.