Bednář was drafted 51st overall by the Los Angeles Kings in the 2001 NHL 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.