First coming into prominence as both author and as the leading lady (in drag) in plays that simultaneously sent up and celebrated classic film genres, Busch appeared in such films as 1984's Vampire Lesbians of Sodom, 1987's Psycho Beach Party, the 1989 The Lady in Question, and Red Scare on Sunset in 1991. Lesser known earlier works in the same vein were Theodora, She-Bitch of Byzantium in 1984, Sleeping Beauty, or Coma also in 1984 and Pardon My Inquisition, or Kiss the Blood Off My Castanets in1986. And, in 1989, for a production staged by the Goodspeed Opera House, revamped the book for the musical Ankles Aweigh.

A performance in the 1993 revival of The Maids resulted from Busch's success in his own works, and in 1994, he took the male lead in his comedy You Should Be So Lucky. His autobiographical one-man show Flipping My Wig in 1996, the serious melodrama Queen Amarantha in 1997, and 1999's Die, Mommie, Die! (made into a feature film of the same name in 2003) rounded out the 1990's.

In 1993 Busch appeared in Addams Family Values, and in 1994's It Could Happen to You. Finding time in his busy acting schedule, Busch penned the 1995 novel Whores of Lost Atlantis, a fictionalized re-telling creation of the Vampire Lesbians of Sodom, before returning to the screen in Trouble on the Corner in 1997, as well as film versions of two of his own plays. These were 2000's Psycho Beach Party (with the exception of Lauren Ambrose playing the "Gidget-type" role Busch originated onstage and Busch playing the part of a policewoman trying to solve the mystery) and Die, Mommie, Die!, for which he won a Sundance Special Performance Award.

Busch's work debuted on Broadway in 2000, when The Tale of the Allergist's Wife opened following an earlier off-Broadway run. The first play in which he did not star, and the first he created for a mainstream audience, Allergist's Wife was written for actress Linda Lavin (TV's "Alice"), who played opposite Michele Lee and Tony Roberts, with Valerie Harper (TV's "Rhoda") and Richard Kind (TV's "Spin City") taking over the lead roles late in the show's run. The Tale of Allergist's Wife ran 777 performances and received a 2001 Tony Award nomination for Best Play. To date, his only other Broadway work has been the rewritten book for Boy George's autobiographical musical Taboo, which only lasted 100 performances.

Busch has performed an annual one-night-only staged reading of his 1984 Christmas play Times Square Angel since 2000, headlined a revival of his 1999 play Shanghai Moon (costarring B. D. Wong) in 2003, and taken the lead in three productions of Auntie Mame: two all-star staged readings in 1998 and 2003 and one scaled-down summer touring production in 2004. Busch's play, Our Leading Lady, about nineteenth-century actress Laura Keene, who starred in the production of Our American Cousin that Abraham Lincoln attended the night he was assassinated in Ford's Theatre, premiered in New York during the 2006-07 season of the Manhattan Theater Club.

On television, Busch played the character of Peg Barlow on the soap opera One Life to Live, and on cable in third and fourth seasons of the HBO series Oz as crossdressing inmate Nat Ginzburg, which has become his best-known role to mainstream audiences.