E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
Money. The word is used in the West Indies for a half pistareen (fivepence). In Jamaica, a bit is worth sixpence, English; in America, 12 1/2 cents; in Ireland, tenpence.
The word is still thieves slang for money generally, and coiners are called bit-makers.
In English we use the word for a coin which is a fraction of a unit. Thus, a shilling being a unit, we have a six-penny bit and threepenny bit (or not in bits but in divers pieces). So, taking a sovereign for a unit, we had seven-shilling bits, etc.