I'm not an expert, but I think the key question is whether the actual metal bumper underneath the painted plastic "bumper [cover]" is intact. That's the part that's actually safety-related and legally mandated equipment.
Depending on your state, you might also be responsible for making sure that all attached parts are properly secured. I had a much smaller incident with my car that left just a corner of the bumper cover loose; it passed inspection in Virginia, but in Maryland there is a specific requirement for bumpers and fenders to be properly secured, and the mechanic wound up reattaching that corner to the fender somehow (not sure how, 90% sure it wasn't to mfr. spec, but it saved me the cost of a new bumper cover!).
In any case, I doubt that any tape-based solution is going to work long term, so if the bumper cover is salvageable and you want to keep it, I'd act sooner rather than later to try to permanently reattach it. Otherwise, check into local regulations as to whether you can drive it with a bumper cover at all?