No, looking at the picture you posted...
Standing at the bumper looking down...
I'd weld a piece of steel from the little piece of the frame that you can see (on top) extending rearward to the edge of the bumper, overlapping the frame and the bumper with once piece of steal. One or two rosette welds in this area probably wouldn't hurt either (depending on how wide the piece of steal used was).
Do the same from the bottom. But looking at your picture, you may not be able too because the frame doesn't match the thickness of the bumper. In that case I'd put a vertical gusset from the frame rail all the way to the back edge of the bumper. That gusset would be trying to accept some of the load from the most aft moment of the bumper and transfer it to the bottom corner of the frame.
With the gussets you talked about and the welded steel plates stated above, and verticle gussets on the bottom,I believe that the only thing left that could fail would be the actual quality of the bumper. Tensile strength would have been added in both lateral and horizontal planes and weight displaced to the bumper instead of the bolts holding the bumper on.
That is what I'd do.
...she started talking about how I never listened to her or somethin, I donno, I wasn't really paying attention...