Driver was born in Westfield, New Jersey, the daughter of Albert and Martha (Miller) Driver. She attended Randolph-Macon Woman's College in Lynchburg, Virginia, graduating with a degree in theatre and classics in 1977. She spent her junior year studying in Athens, and participated in a production by the National Opera of Greece.

Driver made her directorial debut in 1981 with You Are Not I, a short subject film based on a Paul Bowles story and co-written by Jim Jarmusch. Shot in six days on a $12,000 budget, it developed a following soon after a well-received premiere at the Public Theater, only to be pulled out of circulation when a warehouse fire destroyed the film's negative. Rarely seen, it was still championed by renowned critics and film journals like Jonathan Rosenbaum and Cahiers du Cinéma, which hailed You Are Not I as one of the best films of the 1980s. Considered 'lost' for many years, a print was later discovered among Bowles's belongings. Driver was awarded a preservation grant from Women in Film and Television. The restored film screened in the Master Works section of The New York Film Festival 2011.

Driver directed her first feature film, Sleepwalk in 1986. It was awarded the Prix Georges Sadoul (1986) by the Cinémathèque Française, the Special Prize at the 1986 International Filmfestival Mannheim-Heidelberg, and was the opening night selection for the 25th Anniversary of the International Critics' Week (1986) at the Cannes Film Festival. Sleepwalk was also featured at the Museum of Modern Art's 1987 New Directors/New Films Festival and the Sundance Film Festival (1987).

Driver directed the "Bed and Boar" episode of the TV series Monsters (1990). Her second feature film as a Director, When Pigs Fly (1993), stars Marianne Faithfull and Alfred Molina and is scored by Joe Strummer. The film received the Best of Festival Feature award at the 1994 Long Island Film Festival. When Pigs Fly premiered in competition at the Locarno Film Festival, and played a limited engagement at the Lighthouse Cinema on Suffolk Street in New York in 1996.

Driver also wrote and directed the short documentary, The Bowery - Spring, 1994, part of Postcards from New York, an anthology program for French TV. Driver has Producer and production credits for many films of Jim Jarmusch, as well as minor roles in three of his films.

Driver taught directing in NYU's Graduate Film School (1996–1998), where she received her Master of Fine Arts degree in 1982.

Driver has been credited with coining the phrase "necro-tourism" after the surge in tourism in New York due to the fall of the World Trade Towers in 2001.

Driver was a juror at the Buenos Aires International Festival of Independent Cinema (2004) where they also did a retrospective of her films. She was also a juror at the Miami International Film Festival (2005), San Sebastián Film Festival (2006), Bahamas International Film Festival (2006), and Director Emir Kusturica's Küstendorf Film and Music Festival (2010).

Driver has been described as an "often overlooked linchpin of the downtown New York independent film scene." Film critic Luc Sante describes Driver's movies as "doorways into the unknown." Rosenbaum wrote that Driver's films "belong to what the French call la fantastique— a conflation of fantasy with surrealism, science fiction, comics, horror, sword-and-sorcery, and the supernatural that stretches all the way from art cinema to exploitation by way of Hollywood."