Green’s Dictionary of Slang

a person who is wedged between two others, esp. when there is room for only the original couple; thus sit bodkin or ride bodkin, for a coach passenger to ride wedged between two fellows when there is insufficient room for three abreast.

1638		Ford Fancies Act IV: Where but two lie in a bed, you must be Bodkin, bitch-baby must ye?
1798		Loves of the Triangles 182: While the pressed bodkin, punched and squeezed to death, Sweats in the mid-most place [F&H].
1840		Thackeray Shabby Genteel Story (1853) 82: Carry must go bodkin; but she ain’t very big.
1856		G.J. Whyte-Melville Kate Coventry (1865) 111: I would rather give Brilliant a good ‘bucketing’ [...] than go bodkin in a chariot.
1864, 1867, 1870		Hotten Sl. Dict. 79: A small or young person, sitting in the centre, betwen two others, in a carriage, is said ‘to ride bodkin.’ Amongst sporting men, applied to a person who takes his turn between the sheets on alternate nights, when the hotel has twice as many visitors as it can comfortably lodge.
1872		F. Montgomery Thrown Together II 62: The three called a hansom outside, and Cecily [...] sat bodkin .
1882		Sydney Sl. Dict. (2 edn) 1: Anyone sitting between two others in a cab or carriage is said ‘to ride bodkin’.