Career
Bílek began his career at FK Neratovice–Byškovice before being scouted from FK Chmel Blšany in 2003. He played in Blšany three years before being transferred to Football Club Slovan Liberec in 2006. On 7 January 2009, he signed a 3½ year contract with 1.
Football Club Kaiserslautern.
He was suspended for unprofessional behaviour on 30 January 2009. He had trials with Championship side Ipswich Town, and will also spend time with Birmingham City. In January 2012, he transferred to Zagłębie Lubin.