During his career, Bílek was mainly associated with Sparta Prague, which he represented on four separate occasions, starting with the first team aged only 17.
In 1990, he had his first and only abroad experience, in Spain with Real Betis, being relegated in his first season, and returning to Sparta after another year. He then played for FK Viktoria Žižkov and FK Teplice until 2000, appearing once again for his main club in between.
Bílek played for Czechoslovakia, and later briefly for the independent Czech Republic; for both he played a total of 35 matches and scored 11 goals, being an offensive mainstay for the former at the 1990 FIFA World Cup, scoring twice for the quartefinalists.
In late October 2009, after having coached the nation's U19 team seven years earlier, former assistant Bílek was named the new coach of the senior side, following Ivan Hašek's resignation after the failure to qualify for the World Cup in South Africa. He was replaced as the national team boss in September 2013 after nearly four years in the role by Josef Pešice.