Nowadays "bumper" is a misnomer; the reality being a great plastic fairing, affixed to the car with myriad plastic clips, and maybe a bolt or two. Tap nearly anything, and it's likely toast. Or off to the body shop for repair and paint. Or, how about:
Cobble a clip out of unpainted aluminum flashing, to stablilize the two sides at the break? Something like this: (Clip for aligning adjacent plywood edges, just as an example)
