At the 1982 European Championships she finished fourth in the 400 metres hurdles, but won a gold medal in the 4 x 400 metres relay together with teammates Kirsten Siemon, Dagmar Neubauer-Rübsam and Marita Koch. At the 1983 World Championships she finished seventh in the individual event and won another gold medal in the relay, with teammates Gesine Walther, Koch and Neubauer-Rübsam. East Germany boycotted the 1984 Olympics.
At the 1986 European Championships Busch won a silver medal in hurdles and a gold medal in relay. At the 1987 World Championships Busch won two gold medals, both in the hurdles and the relay. At the 1988 Summer Olympics she won another relay medal, this time a bronze medal alongside her teammates Neubauer-Rübsam, Emmelmann and Schersing. She finished in fourth place in the women's final of the 400 m hurdles.
Busch set a world record in the 400 m hurdles in September 1985, with the time 53.55 seconds. It was broken in August 1986 by Marina Stepanova with 53.32. Busch' career best time was 53.24 seconds, achieved in August 1987 in Potsdam. This is the current German record. Her personal best time in the 400 metres was 49.24 seconds, achieved in June 1984 in Erfurt. This places her second on the German all-time list, only behind Marita Koch.