Along with Monk Montgomery and Bob Cranshaw, Swallow was among the first jazz bassists to do so (with much encouragement from Roy Haynes, one of Swallow's favorite drummers). He plays with a pick (made of copper by Hotlicks), and his style involves intricate solos in the upper register. He was one of the early adopters of the high C string on a bass guitar.

From 1974 to 1976, Swallow taught