Burdge was born in Pasadena, California. She attended New York University. In 2013, she had her breakthrough role as Diana Watts in Hannah Fidell's drama film A Teacher, which follows an affair had between a teacher (Burdge) and her student. The film premiered at the Sundance Film Festival on January 20, 2013, and was given a limited release in the United States on September 6, 2013. She has since co-starred in a number of films, including Wild Canaries (2014), The Midnight Swim (2014), The Invitation (2015), 6 Years (2015), and Thirst Street (2017).
