Money. He grappled the cull’s bit; he seized the man’s money. A bit is also the smallest coin in Jamaica, equal to about sixpence sterling.
Definition taken from The 1811 Dictionary of the Vulgar Tongue, originally by Francis Grose.
See also the definition in Nathan Bailey's 1736 dictionary of canting and thieving slang.
To Bishop the Balls * BitchNathan Bailey's 1736 Dictionary of canting and thieving slang
John S. Farmer's collection of canting songs and slang rhymes