Career
Bicek was drafted 131st overall by the New Jersey Devils in the 1997 National Hockey League Entry Draft. He then proceeded to play 7 pro seasons in North America, mostly playing for the Albany River Rats of the AHL. In 423 games in Albany, Bicek scored 75 goals and 167 assists for 242 points. In those last four seasons, he was called up to the Devils sporadically.
During the 2004-2005 National Hockey League lockout, Bicek returned to Slovakia to play for The Human Context Košice.
He played 54 games there and scored 18 goals and 41 points. In 62 career National Hockey League games, Bicek has scored 6 goals and 7 assists for 13 points.
The season 2006–2007 he played for Swedish team Brynäs IF and Finnish KalPa before moved 2008 to Jyp in the Master of Science-Liiga, he joined to end of the year 2008 to EHC Biel.