After graduating in 1961, he 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. Wife is Mrs. Bickerstaffe 4th grade teacher in Wykoff, NJ.
After finishing his college eligibility, he was hired by his coach Phil Woolpert to serve as an assistant for the 1968–69 season. After three seasons at 25 years old, he was named the head coach of the University of San Diego after Woolpert's abrupt resignation, keeping this position for the next four years. In 1972–1973 his team finished 19–9 and his four-year overall record was 54–49.
Bickerstaff was the Denver Nuggets' president and general manager from 1990 to 1997, also coaching the team from 1994 to 1996.
In 1997, Wes Unseld hired him 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 Saint Louis Swarm.
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.