Since the bill was sent directly to you, and since you're worried about how much it costs, I'm guessing you weren't insured at all when this little fender bender took place. Because if you were, you would probably have been smart enough to let them handle it.
Of course there is something you can do about this, in fact you can do exactly what any insurance company would do: Tell them to prove it. Tell them you're not paying anything to anyone until you see a copy of an itemized professional repair estimate and have a chance to look it over.
When they provide you with a copy of the estimate, and they will, then you pay the amount you owe. You can tell them to take you to court, but you'll lose and have to pay all the court costs as well as the original amount. You'll lose because the insurance company has solid documentation, and you have nothing but your uneducated opinion that the repairs shouldn't cost that much. You can probably guess how much your opinion will be worth in court.