Although Bauer had never earned a college degree (despite her years of study), in September 1926, she was hired as an instructor for New York University's music department, becoming their first female music faculty. Among her early colleagues were Albert Stoessel, Gustave Reese, and Percy Grainger. During her tenure at NYU from 1926–1951, Bauer taught classes in composition, form and analysis, aesthetics and criticism, and music history and appreciation, earning the rank of associate professor in 1930. Bauer taught using her own book, the readings from which would then be followed by class discussions. She also advocated strongly for new music and would play “the few pertinent records and piano rolls available,” or have students play unavailable works. Some of her most famous students from her years at NYU included Milton Babbitt, Julia Frances Smith, Miriam Gideon, and conductor Maurice Peress.