Originally from Chicago, Richard Davis began his musical career as a singer with his brothers, singing bass in his family vocal trio. In addition to his earlier years of singing, Richard Davis began studying the double bass in high school with his music theory and band director, Captain Walter Dyett. After high school, Davis studied the double bass with Rudolf Fahsbender of the Chicago Symphony Orchestra while attending Vandercook College. In 1952 Richard Davis received a BME from Vandercook College.
After college, Davis performed in dance bands. The connections he made while performing various gigs led him to meet pianist Don Shirley. In 1954 Davis and Shirley moved to New York city and performed together until 1956, when, Davis began playing with the Sauter-Finegan Orchestra.
In 1957 Davis became a part of Sarah Vaughan's rhythm section, touring and recording with her until 1960. The 60's proved to be a particularly busy and fruitful period for Davis. He was increasingly in demand in a wide variety of musical circles. He worked with many of the cutting edge small jazz groups of the time including those led by Jaki Byard, Eric Dolphy, Booker Ervin, Andrew Hill and Elvin Jones. He was a member of the Thad Jones/Mel Lewis Jazz Orchestra from 1966 until 1972 (now known as the Village Vanguard Orchestra).