Not exactly sure what the bumper is you are refereeing to. Is it one of the white vinyl inflatable type? Similar to this type?
If so 3M 5200 will stick and hold to the vinyl. Repair similar to a bike tube. Find something to bridge the gap 5200 around the hole and press the patch into the 5200. Fill as usual. Of course what ever ate through will do it again.
I think Jeremy's foam idea is pretty good. Spray the foam in the hole, after it sets use the patch and 5200 to make water resistant. The foam will keep it from sinking again.