With German nationality as the daughter of a German businessman, she was born in Switzerland, and resided in Peru for more than 13 years. She was a national champion in Peru at the age of 13, and later moved to Miami, Florida. She dealt with a series of injuries (ear and knee, among others) throughout her career.
Bunge was a professional player from 1978 to 1989, appearing for the first time at No. 150 in July 1978. Her career-high ranking of No. 6 she achieved in 1983. In 1982, she registered her all-time best achievement in Grand Slam singles competition when she reached the semifinals of Wimbledon.
She won four singles tournaments, including the tournaments at the German Open, Houston, and Tokyo in 1982, and Oakland in 1983. She was finalist in Sydney in 1979, Stockholm in 1980, Houston, Tampa, Cincinnati (indoor) and Tokyo in 1981, Mahwah in 1982 and Knokke in 1987.
Bunge won four doubles tournaments, including the tournaments of Pan Pacific in Tokyo with Steffi Graf in 1986 and The Belgian Open with Manuela Maleeva in 1987. She was a finalist at the German Open with Claudia Kohde-Kilsch in 1982, the Swiss Open with Eva Pfaff in 1985, and New England, also Pfaff, in 1987.