I'm wanting to remove the rear bumper off my donor XJ but the bolts seem to be rounded off. What would be another way to remove these bolts?

With a dremel tool you can cut a slot to use a screw driver or grind them off.

If you're talking about the bolts up inside the bumper I'm afraid you're SOL.

You might need to cut the bumper off and get one at a junkyard. There are bolt extractors but that area is tight to work in. Something like this..

http://www.irwin.com/tools/screw-bol...-extractor-set

By cut bumper off I mean cut access panels to those bolts where you can work better. Then you can use suggestion above to cut a slot and use large flat head driver.

I think I might have this all wrong. Are the nuts welded on and the bolt is the one to come off? If so I was attempting to take off the nut. I hope Im wrong.

Yes, the nuts are welded, one of mine isn't but that is because I broke off the original. I'm assuming you mean the bumper bracket to body bolts.

I actually rounded off the nut not knowing it is welded on. bolt is still good.