I've not had much experience with the brake systems on quads but have done several autos and I would think it is much the same. Remove the cover from the ressy on the handle bars, crack the bleeder on the caliper you have been messing with (maybe both if you think air got in the line on the other one as well). Make sure the ressy stays full while you "pump the brakes" until no air comes out of the bleeder. Refill the ressy to full and replace the cap. In my experience this is how you bleed the brakes on a vehicle. There has been talk about an inexpensive vacuum system (mityvac) from your local parts store and a procedure of connecting a hose from the bleeder to a bowl of brake fluid. I have never used either of these methods but if the first method doesn't work (which is obviously the least expensive and simplest), by all means try, try, try again!
Best o luck, chief.
SP