Bishop's big break came when she was cast as the sexy, hard-edged Sheila in the Broadway production of A Chorus Line. Her performance earned her the 1976 Tony Award as "Best Supporting or Featured Actress (Musical)", as well as the 1976 Drama Desk Award for "Outstanding Actress in a Musical". She also acted in the Broadway productions of Six Degrees of Separation, Neil Simon's Proposals, the Tony Award-winning The Last Night of Ballyhoo and Bus Stop. It wasn't long before she was cast opposite Jill Clayburgh in Paul Mazursky's big-screen drama An Unmarried Woman (1978).

In 1986, Bishop was cast for a small part in the film Dirty Dancing, but was then called upon to play a larger role when Lynn Lipton, the actress first cast as Baby's mother, became ill in the first week of shooting. The role was then transferred to Bishop.

Bishop went on to play "mom" to several high-profile stars in numerous features: Howard Stern's in the Betty Thomas-directed comedy Private Parts (1997), and Tobey Maguire's in Wonder Boys (2000). Her additional feature credits include Ich und Er (USA: Me and Him, 1988), Queens Logic (1991), Cafe Society (1995), Miami Rhapsody (1995) and Blue Moon (2002). On television, Bishop starred in the Mike Nichols' series The Thorns and plays Lisa Ann Walter's mother on My Wildest Dreams. She has guest-starred on Law & Order, Law & Order: Special Victims Unit and Murphy Brown.

From 2000 to 2007, Bishop starred in the CW Television Network series Gilmore Girls as the third "girl," Emily Gilmore. Emily is the mother of Lorelai and grandmother of Rory. She plays a wealthy woman who is obsessed with the "proper" New England Society lifestyle. She focuses mainly on charitable functions and how other people view her.