Born in Sydney, Burchmore has been performing since the age of two, trained in singing, acting and dancing and was awarded a scholarship to the University of New England where she majored in Theatre Arts.
She became internationally known for her role as Kate in the 1982 film, The Pirate Movie.
Burchmore gave her first major Australian theatre breakthrough performance in the 1988 production of Sugar Babies opposite Garry McDonald and Broadway theatre performer Eddie Bracken. Later that year, she reprised her role opposite Mickey Rooney and Ann Miller in London's West End theatre production. Whilst in the U.K., she also starred in the revival of Stop the World – I Want to Get Off.
After a string of further stage performances, playwright David Atkins wrote a role especially for Burchmore in his tap dancing musical Hot Shoe Shuffle. Then in 1997, she gave the Crown Casino in Melbourne its opening performance with her very own cabaret spectacular, Red Hot & Rhonda, playing to an audience of over 60,000. The year proved to be big for Burchmore, she also secured a role on Broadway in the Irving Berlin classic, Easter Parade, and later appeared in another show, Stephen Sondheim’s Into the Woods with the Melbourne Theatre Company.
Burchmore released her first album in 1998, self-titled Rhonda Burchmore. To date, she has released a total of four albums; Midnight Rendezvous, Live At The Melbourne Concert Hall, and Pure Imagination. She was also a regular guest on the long-running Australian variety show Hey Hey It's Saturday.
In 1999, Burchmore played the lead role in The Production Company’s first show, Mame. She would also play the title role in Annie Get Your Gun for The Production Company, and later returned in a new production of Mame in 2008.
Further roles followed, including Adelaide in an Australian revival of Guys and Dolls, Tanya in the successful Mamma Mia!, Urinetown The Musical, Tom Foolery, Respect: A Musical Journey of Women, and her own productions; Rhonda Burchmore Sings ‘n Swings, My Funny Valentines and Fever.
Other Australian stage credits include Song and Dance, They're Playing Our Song - as one of the alter egos, and Diana in Lend Me a Tenor. With the Victorian Opera Burchmore won critical acclaim for her performances as Queen of the Fairies in Iolanthe, as Prince Orlofsky in Die Fledermaus with Joan Carden, and in Ruddigore and An Evening with Sondheim.
In 2013, she performed in Trevor Ashley's musical comedy Little Orphan trAshley with Gary Sweet.