Bergsma studied at Stanford University and at the Eastman School, and in 1946 he took a position at the Juilliard School. He participated in the curricular reforms made at the school during the 1940's. He later moved on to the University of Washington, Seattle. A tonal composer, Bergsma's works are lyrical and texturally orthodox, although he is known for his fine technical skills. He later employed avant-garde ideas in his work.