Career
He was drafted in the second round, 27th overall, by the Ottawa Senators in the 1993 National Hockey League Entry Draft. After playing two seasons in the Ontario Hockey League for the Belleville Bulls, Bičánek made his National Hockey League debut with the Senators in the 1994-1995 season, appearing in six games. He went on to spend the entire 1995-1996 season with the Senators" American Hockey League affiliate, the Prince Edward Island Senators.
Bičánek appeared in 21 more National Hockey League games with Ottawa in the 1996-1997 season.
After appearing sparingly for the Senators during the 1997-1998 and 1998-1999 seasons, Bičánek was traded to the Chicago Blackhawks on March 12, 1999, in exchange for a pick in the 1999 National Hockey League Entry Draft. The Blackhawks left him unprotected for the 2000 National Hockey League Expansion Draft, allowing him to be selected by the Columbus Blue Jackets for their inaugural season.
During the 2004-2005 National Hockey League lockout, Bičánek returned to the Czechoslovakian Republic to play for The Human Context JME Znojemští Orli. After five seasons in Znojmo he moved to The Human Context Kometa Brno.