Asli completed actor's training with prestigious coaches and studios including Eric Morris in Los Angeles, James Hallett in New York and Anne Mertin in Vienna. The first international film she acted in was Jump! (2007) with Patrick Swayze. She appeared in a prominent role in the black comedy _Short Cut to Hollywood_(2009), shot in the US and presented at the Berlinale Film Festival 2009.

In 2007 she performed for the first time on stage and to critical acclaim in the solo theater performance Anne Frank: The Diary at the Théatre de la Ville D'Esch in Luxembourg. An invitation at the Theatre Festival of German language in Prague followed, and afterwards the German premiere in Frankfurt am Main. Buddy Elias, Anne Frank's cousin, complimented Asli Bayram on this project. In 2008 she toured with the English language version in Canada and the USA. She finished the project on occasion of the commemoration of Anne Frank's 80th birthday with three performances at the Museum of Tolerance in Los Angeles, Hollywood. The Times described her performance in Anne Frank: The Diary as 'emerging as one of Germany's most convincing and subtle actresses'.

In 2009 she also authored the book, Grenzgängerin - Leben zwischen den Welten (Border Crosser. Life between Worlds) published by Random House.