Hmmmmm. I don’t know of any law that says it’s illegal to drive with tape on your bumper!
I think that you need to have a bumper on your car (if you have a crash and your bumper has fallen off the car and is “over there” somewhere on the other side of the road, then do not drive the car anymore until you get it fixed).
The point of a bumper usually is to provide a crumple zone/impact absorption in the case of a collision; in other words to protect you in a crash.
If you are rear-ended and your car has no bumper, it will probably cause a lot more injury (whiplash) than if your car did have one.
In addition, I’m not sure if there would be liability issues, since I’m pretty sure it is a legal requirement that your car have a bumper on it (as long the car came with one from the factory).
If your bumper was hanging by a thread, and you used 5 rolls of duct tape to put it back in place, then I can’t be sure it’s going to help in the event of a collision.
If you merely backed into a sharp object or a child was playing with some scissors and cut a nice hole, and you have tape on your bumper for mostly cosmetic reasons, then that is obviously less of a problem. In any event, be sure your tail lights, brake lights, and signal lights can easily be seen and are working properly.
Have your bumper repaired as soon as is reasonably possible. At the very least, have your bumper assessed by a body shop to ensure the structural integrity (is it as safe as it could be in the event of a collision).