How to explain this.. A betta bite has about as much pressure as your figure uses to press a key on your computer keyboard.. maybe less. You don't feel a "bite" really, more like something poking you that isn't sharp. An eraser or something. I doubt anyone has ever gotten a bruise or had blood drawn by a betta. It would take a HUGE betta to do that.
They don't have teeth, and as far as them being "Fighting fish" goes, if that's the root of your concern, a betta's tail is very delicate, so if a betta bites a betta tail, it might do damage, but that's like you or I biting a chunk out of toilet paper. Betta fins are easy to damage. Your finger is not.