didn't see anyone mention it but the first thing you want to do BEFORE you bore sight is run both the windage and elevation screws all the way in and all the way out. count the turns and run back in 1/2 way on the windage and 1/3 on the elevation. This will put your crosshairs in the middle of their range (windage) and give you plenty of adjustment for elevation. If the windage screw is all the way in or out, when you adjust elevation you can pull the crosshair right or left. Now boresight and use your coarse adjustment on the rings to get close. I've had good luck just using a lazer pointer ($29 at office max) pushed right into the bore. Use a piece of electrical tape to hold it "on".

Also, you need to be sure the crosshairs are straight and plumb with the center of the rifle.

Good luck