Murray was born in Sydney, New South Wales. At age four, his family moved to Perth, where he was raised. Murray graduated from John Curtin College of the Arts 1988 after gaining a place in the Specially Selected Drama Program. During his time at the College (then John Curtin Senior High School) he performed in many productions and demonstrated a desire to be a professional actor.
Murray went on to pursue an acting career in Australia for several years, including a role in the series headLand. In 1993, he played con man Luke Foster in Neighbours. In 2000, Bartlett relocated to the United States. His first big break there came a few years later, when he was cast as a guest star in the HBO series Sex and the City. He also played D.K., John Crichton’s best friend, in four episodes of the SciFi Channel series Farscape. In 2006, Bartlett toured with Hugh Jackman in the Australian touring company production of Jackman’s Broadway hit The Boy From Oz.
From March 2007 until the show’s cancellation in September 2009, Bartlett was a cast member on the CBS daytime soap opera Guiding Light, where he played Cyrus Foley. He starred as Dominic “Dom” Basaluzzo in the HBO comedy-drama series Looking from 2014 to 2015, and then reprised his role in the series finale television film, Looking: The Movie in 2016. In 2017, he portrayed a recurring role in the musical drama series Nashville. Bartlett assumed the central role of Michael ‘Mouse’ Tolliver in the Netflix revival of Tales of the City.
In 2021, Bartlett starred in The White Lotus as Armond. Bartlett got the role through a self tape audition. For his portrayal, Bartlett received nominations at the Screen Actors Guild Awards and Independent Spirit Awards and won at the AACTA Awards, Critics’ Choice Television Awards, and Primetime Emmy Awards.