Career
He played just 14 games before moving to Plzeň and then returned to play for Sparta for the next season. He then spent the next two seasons playing in Finland"s Master of Science-liiga with spells at Jyp and HIFK where he led the teams in goals and points. National Hockey League career
Bednář was drafted 51st overall by the Los Angeles Kings in the 2001 National Hockey League Entry Draft, but never managed to recapture the form he had in Finland.
He played 37 games for the Kings, scoring 4 goals and 11 assists for 15 points.
On November 26, 2002, Bednář, along with Andreas Lilja was traded to the Florida Panthers for Dmitri Yushkevich, he played 65 games for Florida, scoring 6 goals and 14 assists for 20 points. Overall, Bednář played 102 regular season games, scoring 10 goals and 25 assists for 35 points.
Return to Europe
Bednář moved to Russia during the cancelled 2004-2005 National Hockey League Season and played for Avangard Omsk where he played alongside Jaromír Jágr, Alexander Perezhogin and Oleg Tverdovsky. In 2005, Bednář returned to Slavia Prague where he has become one of their core players and left the team after four years on 29 April 2009 to sign with Atlant Moscow of the Kontinental Hockey League.
In 2010, Bednář signed a one-year contract with The Human Context Davos from the Swiss National Lawyers Association where he played alongside 3 other Czechoslovakian players: Petr Sykora, Petr Taticek and Josef Marha.
During the 2010-2011 regular season, Bednář scored 35 goals and 15 assists for a total of 50 points in 43 games.