I agree that it is not your control arms, but if it were, then $800 sounds about right. That should be the out the door price including a 4 wheel alignment.
Bouncing all over the place could be due to bad struts or excess air pressure in the tires. Cold air pressure should be no more than 35 psi. The temp for cold air is 72?F. Drop 1 psi for every 24?F below this temp. Check your door panel for the recommended pressure.