Buring was born in Sweden but grew up in the Middle East. She attended high school at the American British Academy in Muscat, Oman with actor and producer Stegath Dorr, who was a childhood friend. When she turned 16, she moved to England. Buring graduated from the London Academy of Music and Dramatic Art in 2004. She is also the associate director of the MahWaff Theatre Company.
In 2006, Buring guest-starred in "The Impossible Planet", the first episode of a two-episode Doctor Who story. Her character, Scooti, perished in the vacuum of space; the scenes of her body floating towards a black hole were filmed in an underwater tank in Pinewood Studios, to create the effect of weightlessness. Buring also starred as Debbie in Much Ado About Nothing (BBC1), Midsomer Murders (ITV), Casualty (BBC1) and Murder Prevention (Channel 5). In 2012 she starred in White Heat, Blackout and The Poison Tree. She also starred as Long Susan in Ripper Street and as the scheming Edna Braithwaite in Downton Abbey.
Also in 2006, Buring played Olivia in a production of Shakespeare's Twelfth Night by Exeter's Northcott Theatre Company, alongside Sara Weymouth and David Gwillim, and appeared in a new play, Seduced by Michael Kingsbury at London's Finborough Theatre. For MahWaff Theatre Company, she starred in Guardians, Monologue For An Ensemble, and An Inspector Calls. She is currently starring in Strangers on a Train at the Gielgud Theatre, London until March 2014.
In her first film role, Buring starred in The Descent by director Neil Marshall. She appeared in the sequel in 2009. She starred in the 2008 film Doomsday, linking her again with her Descent director Neil Marshall. Buring also starred as Alice in the independent film Credo, also known as The Devil's Curse. In 2009, Buring appeared as the female lead in the film Lesbian Vampire Killers opposite James Corden and Mathew Horne. In May 2010 she appeared as Jozefa in Witchville for SyFy alongside Sarah Douglas. In 2011 MyAnna appeared as Shel in Kill List. In 2014 she will appear in Epic.