In 1987, Bykova won a silver medal at the World Championships in Rome, with a clearance of 2.04 metres. The winner was Stefka Kostadinova of Bulgaria, with a new world record of 2.09 metres. At the 1988 Olympic Games in Seoul, Bykova won the bronze medal with 1.99 metres, behind the American gold medal winner Louise Ritter and the silver medallist Kostadinova.