In the highly popular game Grand Theft Auto, you get the trophy/badge Three-Bit Gangster at level six. Which, as you suggest, would seem to mean that you're one level above a two-bit gangster.

As you guessed, "three bits" means cheap. A "bit" is an old fashioned slang term for an amount of money. 8 bits is a dollar. 2 bits is a $0.25 or a quarter. But when the term is used like the speaker used it, it just means low quality and cheap. It is not supposed to be a direct comparison to anything.

Thank you!

Two bits is the correct term historically. Three bits......no clue. Maybe the speaker just wanted to update the term two bit. Originally two bits was 12 1/2 cents. It then came to represent 25 cents. So yes, it means cheap, unworthy or half-assed.

@Jerry Sorry, I updated the link. He is from UK.