Jensen trained at Queen Margaret University, Edinburgh.

Her first big television role was as eccentric secretary Rosie McConnichy in the final series of BBC comedy May to December, as a replacement for the character of secretary Hilary. In 1994 she played Heather in Roughnecks, a BBC television series based around the workers on a North Sea Oil platform. In 1996 she played Clare Donnelly, the daughter of Glasgow criminal Jo-Jo Donnelly (played by Billy Connolly) in the BBC drama Down Among the Big Boys. She then appeared as Fiona Morris in EastEnders. Jensen also had a small role in a Dangerfield episode called "Contact," in which she played the mother of a young girl with meningitis.

Jensen starred alongside Ricky Gervais in the BBC Two/HBO television programme Extras as the socially inept Maggie Jacobs. For her work on the first series, she received best television comedy actress and newcomer awards at the 2005 British Comedy Awards. In 2006, Jensen received two British Comedy Awards and a BAFTA nomination for her role in Extras. Her role in the 2007 Christmas Special earned her an Emmy Award nomination.

In January 2006 she starred in the short-lived drama series Eleventh Hour on ITV1, alongside Patrick Stewart. Stewart had also appeared in an episode of Extras. Later that year she played Steve Coogan's agent in A Cock and Bull Story. In 2007, she provided the narration for the UK film Taking Liberties, directed by Chris Atkins.

In September 2006, Jensen began her role as Christina McKinney on the ABC series Ugly Betty. Her character in Ugly Betty was originally an American, but when she met with the show's producers they liked Jensen's accent and decided to change the nationality of the character. After three years, as of 7 May 2009, Jensen left Ugly Betty because of location conflicts after the show's production moved to New York from Los Angeles in summer 2008. However, she remained as a recurring member of the cast.

In January 2009, Jensen starred in No Holds Bard, a BBC Scotland one-off special comedy shown on Burns Night as part of a line-up of special programming to mark the 250th Birthday of Robert Burns. She is the narrator of Channel 4's Embarrassing Illnesses and Embarrassing Bodies. She also narrates Bank of Scotland's current advertisement campaign and Persil detergent adverts for both television and radio.

In September 2009 until its cancellation in May 2010 she co-starred alongside Jenna Elfman in the sitcom Accidentally on Purpose as Olivia.

Jensen starred in BBC comedy Nativity as Jennifer Lore, a Hollywood producer. Nativity was released in cinemas on the 27 November 2009.

Ashley Samantha Jensen was born to Margaret and Ivar Jensen and raised single-handedly by her mother, a special-needs teacher living in Annan, Scotland. She has no contact with her father and is very private about the matter. In June 2008 Jensen's father claimed that she has a half-sister, Gillian, whom she has never met

After six years together, Jensen married English actor Terence Beesley in a ceremony in the woods of Big Sur, California on 29 January 2007. They met in 1999 while working on a stage production of King Lear. The couple live with their dog Barney in Los Angeles, USA and have a flat in Holland Park, west London. The couple also own property in Umbria, Italy. The couple had their first child together, a boy called Francis Jonathan Beesley, on 20 October 2009.