Bykova was born in Azov, Rostov, Russia and first came to international attention at the 1980 Olympic Games in Moscow, where she finished ninth in the final with 1.88 meters.

The record would stand for only a month, as Bulgaria's Lyudmila Andonova cleared 2.07 metres in July.

Bykova was prevented from competing at the 1984 Olympic Games in Los Angeles due to the Soviet boycott.

In 1987, Bykova won a silver medal at the World Championships in Rome, with a clearance of 2.04 metres.

Bykova received a three-month ban when she tested positive for the drug ephedrine at the Goodwill Games in 1990, and missed the European Championships held later that year.