Bock earned Tony Awards for both Fiddler on the Roof and Fiorello!, which also earned a Pulitzer for the composer and his collaborator, Sheldon Harnick. Bock's first major Broadway credit was the Sammy Davis, Jr. vehicle Mr. Wonderful, which he wrote with Larry Holofcener and George Weiss. His next Broadway outing was The Body Beautiful, his first collaboration with Harnick. Their other musicals include Tenderloin, She Loves Me, and The Rothschilds. The pair also contributed music to the plays Never Too Late and Man in the Moon.
The Bock and Harnick partnership dissolved after their collaboration on The Rothschilds in 1970, and they reunited only once to create the new song "Topsy Turvy" for David Leveaux's revival of Fiddler on the Roof in 2004.
Born in New Haven, Bock went to college at the University of Wisconsin, where he met Holofcener. After graduation, the two returned to New York and joined the staff of The Admiral Broadway Revue, which later became Your Show of Shows, where they wrote songs for the show's stars, Sid Caesar and Imogene Coca, as well as the chorus and the Corps de Ballet.
Bock's additional honors include a Daytime Emmy Award, shared with Billy Aronson, for the song "A Fiddler Crab Am I," used on the animated series The Wonder Pets. In addition, Bock was inducted into the Songwriters Hall of Fame in 1972.