Bunbury originally worked as a model, and began acting at her agency's suggestion.

[14] Bunbury portrayed Eva in the science fiction CBS television series Under the Dome.

[15] Bunbury starred in the Fox drama series Pitch, where she portrayed the (fictional) first female player in Major League Baseball.

[19] In 2020, Bunbury was in the main cast[20] for the Peacock adaptation of Aldous Huxley's Brave New World.

That same year, she began playing Cassie Dewell in the ABC crime drama series Big Sky.