 Bunyan was born in Aruba, the eldest of three daughters, and settled in Milwaukee, Wisconsin with her family when she was 11.After the death of her mother Wilhelmina, a nurse, Bunyan and her family continued to pursue educational opportunities; at one point, all of the members of the immediate family were enrolled at local colleges and universities, each studying for an undergraduate degree.Bunyan started her journalism career freelancing at the "Milwaukee Journal" while attending the University of Wisconsin–Milwaukee nearby, then went on to television jobs at WGBH-TV in Boston and WCBS-TV in New York City before arriving in Washington in 1973 and joining WTOP-TV (now WUSA-TV), a station that was known for its Eyewitness News team that included Max Robinson, Gordon Peterson and Warner Wolf.