The answer is no, you can't drive without a bumper or hood. Your vehicle would be considered unsafe.
Front bumper is always required and has to be in good operating condition (eg: no exposed sharp edges, collapsed portions, etc.).
If you hit a pedestrian, the idea is that there's a bumper to absorb most of the impact. It's not in their interest to be hit on an unfinished portion of a vehicle that may leave them exposed to sharp edges. That and they don't want to end up tangled in your engine bay because you have no hood.