Try getting an open end wrench on the bolt. It may take a little working around to get it onto 2 opposite flats, but if you can and are able to apply a litte pressure, when the bolt turns it will force the locking tabs away from the bolt head and you then will be able to get a socket on it to remove the bolt.
If that doesn't work, you can use a long thin chisel or screwdriver and you should be able to get at the tabs on the locking plates by reaching thru from the opposite side. Once you bend the tabs out a little, You can use a ratchet and long extension to reach thru and remove the bolt.
After you get the bolts out, and remove the bumper, reverse the order and reinstall the bolts. With the bolts in and tight, use the long punch again to rebend the lock tabs back against the flats of the bolt head.
Very important to use the lock tabs to safety lock those bolts in place.