Busch was born in New York City, New York, the son of Gertrude (née Young), a homemaker, and Benjiman Busch, a merchant.

Busch first came to prominence as both author and performer (as the leading lady, in drag) in plays that simultaneously sent up and celebrated classic film genres. These include Vampire Lesbians of Sodom (1984), Psycho Beach Party (1987), The Lady in Question (1989), and Red Scare on Sunset (1991). Less well-known are some earlier works in the same vein: Theodora, She-Bitch of Byzantium (1984), Sleeping Beauty, or Coma (1984) and Pardon My Inquisition, or Kiss the Blood Off My Castanets (1986). He revamped the book for the musical Ankles Aweigh for an 1989 production staged by the Goodspeed Opera House.

Busch's success in his own works led to his performance in a 1993 revival of Genet's The Maids. In 1994, he took the male lead in his comedy You Should Be So Lucky. Other works of the 1990s include his autobiographical one-man show Flipping My Wig (1996) and a serious valentine to melodrama Queen Amarantha (1997). His 1999 play Die, Mommie, Die! was performed in Los Angeles and was made into the 2003 feature film of the same name.

Busch's film appearances include Addams Family Values (1993), It Could Happen to You (1994) and Trouble on the Corner (1997). Busch has twice appeared in film versions of his own plays: 2000's Psycho Beach Party (with Lauren Ambrose playing the Gidget role Busch originated onstage and Busch playing the new part of the policewoman trying to solve the mystery) and Die, Mommie, Die!, for which he won a Sundance Special Performance Award. He co-wrote, starred and directed the film A Very Serious Person (2006), which premiered at the Tribeca Film Festival and starred Polly Bergen, where it won an honorable mention. He is also the subject of the documentary The Lady in Question is Charles Busch (2006).

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

Since 2000, Busch has performed an annual one-night-only staged reading of his 1984 Christmas play Times Square Angel. In 2003, he headlined a revival of his 1999 play Shanghai Moon (costarring B. D. Wong). He has taken the eponymous lead in three productions of Auntie Mame, two of them all-star staged readings (fall 1998 and 2003) and one a scaled-down summer touring production (2004).

Our Leading Lady, Busch's play about Laura Keene, the nineteenth-century actress who starred in the production of Our American Cousin that Abraham Lincoln attended the night he was assassinated in Ford's Theatre, is premiered in New York during the 2006-2007 season of the Manhattan Theater Club.

His play, "The Third Story," premiered at the LaJolla Playhouse in 2008 and was then produced in New York by MCC Theatre at the Lortel Theatre with Busch and co-star Kathleen Turner.

On TV, Busch has played the characters of Peg Barlow on One Life to Live and, in his best-known role to mainstream audiences, crossdressing inmate Nat Ginzburg in the third and fourth seasons of Oz.

Busch is the author of the 1995 novel Whores of Lost Atlantis, a fictionalized re-telling of the creation of Vampire Lesbians of Sodom.