Green’s Dictionary of Slang

(US) to live together, usu. of men, but occas. also of male/female couples.

1960		P. Oliver Blues Fell this Morning 101: Unions may be casually made, with couples ‘batching up’ with little ceremony.
2000		(con. 1910s) R. McBee Dance Hall Days n.p.: Devich [...] immigrated to the United States in 1913 [where] he ‘bached’ up with other miners and timber workers.
2012		BBC Radio 4 14 June [radio] You need two people to bach up together — it’s very much a buddy buddy system.