Bundy has appeared on almost a hundred television shows. She is best known as a soap-opera actress, appearing as a regular in both General Hospital and Days of our Lives. In 1965 she and Walter Koenig appeared together on the series Gidget ("Gidget's Foreign Policy"). She was in the 1968 western film Firecreek with Gary Lockwood and Barbara Luna. In 1974 she appeared opposite William Shatner in an episode of The Magician ("The Illusion of the Queen's Gambit"). She acted with Shatner again in the made-for-television movie Crash (1978).