After graduating in 1961, Bickerstaff moved to Cleveland where he had relatives, with the idea of joining the Army, but he instead accepted a basketball scholarship to play for Rio Grande College. The racial tension he experienced during his time playing there made him leave school early and head back to Cleveland to work in a steel mill. However, the difficult working conditions prompted him to accept a second opportunity to play college basketball at the University of San Diego from 1964 to 1966. As a senior, he was named team captain and MVP, when the Toreros finished 17-11 and went on to play at the Small College Regional Playoffs. He is a member of the Kappa Alpha Psi fraternity.

In 1973, Bickerstaff was hired as an assistant for the Washington Bullets by then coach K. C. Jones and was a part of the 1978 Bullets NBA Championship. He left the team after 12 seasons, when Lenny Wilkens hired him for the head coaching position with the Seattle SuperSonics (1985–1990), reaching the Western Conference Finals in 1987.

In 1997, Wes Unseld hired Bickerstaff to coach the Bullets, making the playoffs for the first time since 1988 and becoming the league’s all-time 34th-winningest coach. After parting ways with the team in 1999, he had a two-year stint with the International Basketball League’s St. Louis Swarm. Bickerstaff was twice named IBL Coach of the Year.

In 2003, Bickerstaff was hired by Ed Tapscott to become the expansion Charlotte Bobcats’ first head coach and general manager.

Bickerstaff was hired by the Los Angeles Lakers in 2012–13 as an assistant coach to Mike Brown. On November 9, 2012, Bickerstaff was named interim head coach of the Lakers after Brown was fired. Three days later, the Lakers signed former Knicks coach Mike D’Antoni as their official head coach, although D’Antoni’s on-court debut was delayed as he recovered from knee-replacement surgery. Bickerstaff continued to coach the Lakers in D’Antoni’s absence, ending his stint with a 4–1 record, the highest winning percentage in Lakers’ history, albeit in only five games. He continued with the team as an assistant coach, but was fired after the season.