I think Bradfors showed a way of using the Bingham jig that really made it do a pretty good job of aligning the limbs. It worked well for us. Are your pin and bolt the same distance apart as the jig?
If so, I would try drilling the bolt first. Once the bolt is drilled and your bushing installed, I would line the jig up on the riser pad and screw it down, as close to center as possible. From there use a long 5/16" bolt to screw your limb through the jig and into the bushing on your riser. You can then line up the pin into the pin hole. I would tape the belly of the limb and draw a center line down the limb, before attaching it to the riser.
Check the limb for allignment using a string clamped to the limp tip and run it down the belly of the limb through the center line drawn on the riser. Adjust the (undrilled) point end of the jig to make sure your line runs down the center line drawn on your limb and riser. Measure twice before drilling. Repeat on the other limb.
I hope that makes sense and if you have any questions let me know. If your point and bolt don't line up with the jig I am not sure the best way to handle it then. The bingham jig isn't inherently square because of its adjustability. IF you realize that it can still be helpful lining things up. Once again I hope that helps, and I am not an accomplished bowyer or nearly as talented as others on here so hopefully someone else will have some advise.
Good luck and take your time!