Known for an understated, restrained style of playing, Drummond performed and recorded with country and R&B stars in the 1960s in South Carolina, Illinois and, later in the decade, Cincinnati, Ohio. He played rockabilly with Conway Twitty, funk with James Brown and vintage R&B with Hank Ballard before moving to Nashville where he played on sessions with Joe Simon, Fenton Robinson, Jimmy Buffett and Charlie Daniels, among others.
When Young traveled to Nashville to work on Harvest, Drummond visited the studio and became a member of the Stray Gators with the drummer Kenny Buttery and pedal steel guitarist Ben Keith. Drummond would continue to record and tour with Young on albums and concerts that did not involve his primary backing band Crazy Horse. He also toured with Crosby, Stills, Nash & Young as well as record and tour with CSN and the duo of Crosby and Nash.
Moving to California led to Drummond becoming one of the most in-demand session bassists, often paired with drummer Jim Keltner. Together they were the rhythm section on CSNY's 1974 tour, during which time Drummond met Dylan. He would later join his band during during Dylan's Christian gospel phase, co-writing "Saved." Drummond also appears on multiple albums by J.J. Cale, Ry Cooder and Graham Nash, and played on hit records by Don Henley, Bette Midler, Paula Abdul and Jewel.