Green’s Dictionary of Slang

to pair off, to form a relationship; to pick up a sexual partner.

1958		C. Lee diary 18 Apr. in Eight Bells & Top Masts (2001) 101: The Third [Engineer] never bags off. he has a picture of his wife on his desk and says goodnight to her every night.
1993		I. Welsh Trainspotting 131: Renton and Spud are horrified to note that Begbie has bagged off.
2000		N. Griffiths Grits 352: Al get yer rat-arsed an bagged off with some buxom dairymaid called Rhiannon, irrull be fuckin top, man.
2004		P. Howard PS, I Scored the Bridesmaids 29: I bagged off with that Emily Patten.