Moore started on bass at age 15, at Withrow High School in Cincinnati, where he performed in various ensembles as well as the Presentation Orchestra in George G. "Smittie" Smith's famed The Withrow Minstrels.

He played with his father in nightclubs in Cincinnati. He attended the Cincinnati College Conservatory, playing with Cal Collins and Woody Evans locally. He toured Africa and Europe with Woody Herman in 1966, and recorded with Dusko Goykovich while in Belgrade.