[1][2] Bassett went on her first audition at 14, landed the lead role in the Australian Theatre for Young People's production of Romeo and Juliet,[3] moving on to study, write, and perform at the National Institute of Dramatic Art.

[5] Bassett landed the lead in the MTV film Dungoona (2009) and appeared on several Australian television series, Rake (2010), Wild Boys (2011), and Cops L.A.C.

Hogan's film Mental (2012), alongside Toni Collette and Liev Schreiber, and traveled to Paris to play the lead in the feature, The Last Goodbye (2013).

[9][10] Shortly after landing, she booked Fox network sitcom No Place Like Home[11] and made her "breakout role” as 50s-era starlet Gloria DeLamour in the Coen Bros' Hail, Caesar!

[12][13] Bassett continued to play several film roles in the United States starring in thrillers, House by the Lake, The Pale Door, Desolate, Spinning Man, opposite Guy Pearce, Pierce Brosnan and Minnie Driver, and indie drama Katie Says Goodbye with Mary Steenburgen, as well as comedy film Spy Intervention, ABC series Operation Buffalo and 12 Mighty Orphans with Luke Wilson, Martin Sheen and Robert Duvall.