He spent nine seasons in the National Hockey League (NHL), playing with the Washington Capitals, Montreal Canadiens, and Vancouver Canucks.

He has played for the Vancouver Canucks, Montreal Canadiens, Washington Capitals, AHL Portland Pirates, IHL Cincinnati Cyclones, OHL Kingston Frontenacs and Barrie Colts.

On March 13 of 2001, Bulis was traded from the Washington Capitals along with Richard Zedník and a first round pick (Alexander Perezhogin) to the Montreal Canadiens for Dainius Zubrus, Trevor Linden and a second round draft pick (later traded to the Tampa Bay Lightning, who selected Andreas Holmqvist).

Bulis recorded his best NHL season in 2005–06 with Montreal where he scored 20 goals and 20 assists for 40 points in 73 games played.

During the campaign in December 2005, Bulis was named to the Czech national ice hockey team for the 2006 Winter Olympics in Turin.