A bit was 12.5 cents. It goes back to an eighth of a dollar based on the original Spanish piece of eight which was the original basis of the US dollar.
Two bits was 1/4 dollar, or 1/4 of a Spanish coin.
It all goes back to silver coins.
You nailed it, sir. I mentioned it for younger readers to understand.
"Two bits
Four bits
Eight bits
A dollar"