Bursill made her television debut in 1973, appearing in the lead role of short-lived comedy series The People Next Door as Meg Penrose.

She was a regular character in daily soap opera The Unisexers which was launched in February 1975 on the Nine Network, however the program's low ratings led to its cancellation and removal from broadcast after only three weeks.

After departing the series, Bursill appeared in several recurring roles; in A Country Practice as Bianca Forbes-Hamilton (1981) and Cecily Day (1985), Hey Dad..!

[3] Bursill made her feature film debut in 1975 when she was cast in The Great Macarthy, a sports comedy with John Jarratt and Barry Humphries.

In 1987, she starred in Jilted, which earned her an Australian Film Institute Awards for Best Actress in a Supporting Role.

Further film credits include Afraid to Dance, Spider and Rose, Billy's Holiday, The Goddess of 1967, Son of the Mask, Three Blind Mice, Random 8, and Wish You Were Here.