Burns' major television role was her performance in the cult television program Prisoner (known internationally as Prisoner: Cell Block H), in which she played the tough but affable lesbian bikie character, Frieda "Franky" Doyle. Although only appearing in the first 20 episodes, her character attained cult status, resulting in her winning a Logie Award for Best Lead Actress in a Series. Burns stated in a 2011 interview that she left the show due to very low pay and an increased workload as a result of the more rapid production of episodes. She also stated that it was her decision to be killed off as she did not want to be lured back. After Burns's departure from the series the producers released a telemovie titled The Franky Doyle Story which they compiled using footage from the episodes in which Burns had participated.
Burns, an experienced and versatile theatre actress, went to the UK and appeared in numerous West End theatre productions and had roles in TV series such as The Bill, Taggart and Heartbeat. Burns also appeared in films, particularly during the late 1970s and 1980s, including The Mango Tree (1977), Bad Blood (1981), Starstruck(1982) and Strikebound (1984)
Burns was married to Alan Lawrence, a British-born musician and composer, for 36 years. She died on 22 December 2015, after a brief cancer illness at the Princess Alexandra Hospital in Brisbane at the age of 68.