Bichette played in the MLB as an outfielder for the California Angels (1988–1990), Milwaukee Brewers (1991–1992), Colorado Rockies (1993–1999), Cincinnati Reds (2000), and Boston Red Sox (2000–2001).
Bichette was a four-time All-Star as a member of the Rockies. He also won the Silver Slugger Award in 1995.
Since his retirement as a player, Bichette was hired in 2012 to become the hitting coach of the Rockies.
