Reid was raised in Sacramento, California, where he played the trumpet through junior high and high school. Upon graduation from Sacramento High School, he entered the United States Air Force as a trumpet player. During that period he began to be seriously interested in the bass.
After fulfilling his duties in the military, Rufus had decided he wanted to pursue a career as a professional bassist. He moved to Seattle, Washington, where he began serious study with James Harnett of the Seattle Symphony. He continued his education at Northwestern University in Evanston, Illinois, where he studied with Warren Benfield and principal bassist, Joseph Guastefeste, both of the Chicago Symphony. He graduated in 1971 with a Bachelor of Music Degree as a Performance Major on the Double Bass.