The St. Louis native moved to New York City in the early 1960s and soon began to run with an artistic downtown crowd. He became associated with Theatre Genesis, one of the leading lights in the Off-Off-Broadway movement of the time. Founded by Ralph Cook at St. Mark's-Church-in-the-Bowery, Genesis devoted itself to nurturing new playwriting talents, including Shepard.

Mr. Hart directed Shepard's early work Shaved Splits at La MaMa in 1971. The two men were close enough that Mr. Hart was best man at Shepard's marriage to actress O-Lan Jones, which took place at St. Mark's Church. Afterwards, the Shepards and Mr. Hart lived in the same building on Sixth Avenue.

Mr. Hart also collaborated with such artists as Joseph Chaikin, who founded the Open Theatre, and Robert DeNiro, whom he directed in an 1986 production of Reinaldo Povod's Cuba and His Teddy Bear. The show began Off-Broadway and transferred to Broadway in 1986. It was the director's only Broadway credit. He was director of Nicky Paraiso's 20th Century Blues at La MaMa in 1988.

He returned to the work of Shepard in 1996, when he stage a revival of a revised version of the playwright's The Tooth of Crime at Second Stage. In 1991, Mr. Hart staged the premiere of Shepard's abstract, anti-war drama States of Shock at An American Place. The production, starring John Malkovich, was largely panned. However, Frank Rich in the New York Times wrote "Bill Hart's energetic, tightly focused production is blameless for the lulls."

Mr. Hart also remained a part of the art world, becoming in the 1970s the director of the Razor Gallery in SoHo. The following decade, in an unlikely turn, he was named the literary manager of Joseph Papp's Public Theatre. According to the Times, one of his first projects was the development of Larry Kramer's Normal Heart, an AIDS drama that became a major hit.