Green’s Dictionary of Slang

(US) a bisexual.

1966		Trimble 5000 Adult Sex Words and Phrases.
1972		B. Rodgers Queens’ Vernacular.

a woman who is amenable to vaginal and anal or vaginal and oral intercourse.

1939		D. Maurer ‘Prostitutes and Criminal Argots’ in Lang. Und. (1981) 117/2: two-way girl. A prostitute who takes intercourse normally or through the mouth.
1954		(con. 1937) C. Chessman Cell 2455 96: He narrated, in elaborate detail, how he converted them into ‘two-way bitches.’.
1958		(con. 1930s) Murtagh & Harris Cast the First Stone 198: The two-girl houses gave [customers] a choice between a blonde and a red-head [...] both of them played up as ‘two-wayers’ who would meet all requests.

a male prostitute who is willing to act as passive or active partner in sodomy or fellatio.

1919		Transcript Foster Inq. in L.R. Murphy Perverts by Official Order (1989) 11: ‘Galli Gurci,’ was a ‘two-way artist,’ who ‘could be screwed in the rectum and also took it in the mouth.’.
1941		G. Legman ‘Lang. of Homosexuality’ Appendix VII in Henry Sex Variants.
1965		Guild Dict. Homosexual Terms 46: two-way man (n.): A male prostitute who, if heterosexual, will turn over, after fellation, and allow himself to be pedicated; and, if homosexual, will also perform fellation.
1972		B. Rodgers Queens’ Vernacular 112: Hustlers too have their sexual proclivities: a goofer (’40s) [...] allows only his cock to be the currency of sexual sale, while a two-way man is obviously more flexible.