Could this have been the old Spanish/Mexican peso/dollar/piece of eight? IIRC, when the USD was first introduced it was pegged to the Spanish piece of eight (which was worth 8 reales) at 1..1, so one real was worth 1/8 of a USD. The real coin was colloquially known as a bit in some English speaking areas, and two of them were equal to a “real” US Mint issued quarter, and 25 cents became colloquially known as two bits, hence the expression.