He attended Lincoln Junior High School where he took up tennis practicing by hitting the ball against the garage door.

Bassett was the co-captain (with Herb Flam) of the University of California at Los Angeles tennis team that won the NCAA championship 1950.

Also in 1950, he won the singles title at the Cincinnati Masters, defeating Ham Richardson in the final in four sets.

Bassett won the Pacific Northwest Championships in Tacoma, Washington in 1956 and 1958 and the West Hollywood Championships at Plummer Park[2] in West Hollywood in 1958 (defeating Norm Perry in the final), 1959, and 1960 (defeating Vladimir Petrović in the final).

While at UCLA, Bassett worked with some of tennis’ most recognized players, including national champions Arthur Ashe, Ian Crookenden, Billy Martin and Jimmy Connors, and 1992 Olympian Mark Knowles.