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.
Originally a reporter and weekend co-anchor with Patrick McGrath, Bunyan was promoted to co-anchor alongside Gordon Peterson at 6 p.m. after Robinson joined ABC News in 1978 (she would add the 11 p.m. newscast a decade later) and settled in as a member of a local news team that also included sportscaster Glenn Brenner and meteorologist Gordon Barnes.
In addition to reporting on major local, national and international stories, she also hosted the award-winning magazine programs 22:26 and Studio Nine.
On December 11, 1995, after the management at WUSA offered her an anchor demotion and salary cut to stay at the station,[8] Bunyan surprised viewers when she announced her resignation on the air during the 6 p.m. news.
Bunyan briefly worked for MSNBC and ran a public relations firm for a few years before returning to the Washington airwaves in February 1999, replacing Paul Berry as the lead anchor at WJLA-TV.