If you take out those two bolts, plus the ones on the side, that panel comes off. There are a couple layers in there and the nuts are captured on the back and sandwich them all together. You're going to have to keep disassembling until you're able to get to the back and weld the nut back in place.
If you got the bolt broke lose before the nut popped, you might be able to stick the screwdriver behind the bolt head and pry outwards (careful of the paint...) to keep the nut in place well enough to get the bolt out. If not, you're going to be in trouble. But even if that works, it is going to be a long, slow, pain in the butt process. I'd probably cut the head off the bolt. The panel will come off over the bolt-stub. You're going to really have to be careful of your paint, too.
If you can't get behind it to cut off the head, you might have to get the rest of it loose and try to rotate it far enough out of the way to get a hacksaw blade in behind it, or see if it's possible to grab the nut with some vise grips.
Good luck.