Bičánek was drafted 27th overall in the 1993 NHL Entry Draft by the Ottawa Senators. Bičánek played 4 seasons with the Senators before being traded to the Chicago Blackhawks for a pick in the 1999 NHL Entry Draft on March 12, 1999.He played 2 seasons with the Blackhawks before being picked up by the Columbus Blue Jackets. He played 2 seasons with the Blue Jackets before returning to the Czech Republic because of the 2004–05 NHL lockout. He played for the Orli Znojmo of the Czech Extraliga for 5 seasons before leaving and joining HC Kometa Brno.