Bostwick replaced C.C. Courtney in the musical Salvation. His next stage appearance was in the 1971 rock opera Soon, which closed after three performances. In 1972, Bostwick originated the role of bad boy Danny Zuko in the stage production of Grease, earning a Tony Award nomination for his performance. This was followed by a voice role as Terr in the English-dubbed version of Fantastic Planet in 1973. He later starred with Tim Curry and Susan Sarandon in The Rocky Horror Picture Show (1975) portraying the character of Brad Majors. He also won a Tony Award for his performance in the 1977 musical The Robber Bridegroom. In 1981, Bostwick starred in the TV series adaptation of the 1978 movie Foul Play, with his role modeled after Chevy Chase's and co-star Deborah Raffin in Goldie Hawn's part. The following year, he starred in Megaforce. Bostwick starred, along with Carl Weintraub, as Rick Armstrong in the short-lived ABC sitcom Dads during the 1986–87 season. From 1996 to 2002, Bostwick portrayed Randall Winston, the mayor of New York City in the sitcom Spin City opposite Michael J. Fox and his successor, Charlie Sheen. In 2006, Bostwick replaced Peter Scolari as Mr. Tyler, the father of Amanda Bynes' and Jennie Garth's lead characters, on What I Like About You.