I've never seen a rat "know where to bite" a snake.... If given the opportunity while being constricted, they will chew and grab onto anything that is close to their mouth in an attempt to be released, but most of my snakes grab the rat in a way that this cannot happen, they move their coil out of the way if the teeth are close, or I'm standing there with a spoon to stick between the rat's teeth and snake's skin.
If supervised, the chance of serious (or even minor) injury to your snake is incredibly unlikely (I only ever step in to assist with LARGE rats.. I've seen many of my snakes get bit and have no bite wounds - they're tougher than people give them credit for).
There is no problem with feeding mice to a ball python, but keep in mind as they get larger, you'll be spending $2-5 per mouse (depending on where you're getting them) AND need to feed multiple mice ($15 or more purchase) vs. feeding a single appropriately sized rat ($3-$10 depending on where you're getting them)... that's if your snake will take multiple prey items in one sitting.