Welcome to the forum!

Actually a bare plastic floor in the cage is perfectly fine. It’s what we would recommend while you’re litter training him.
Once he’s neutered and litter trained some members might suggest putting towels on the floor for him, but he doesn’t need them, and it won’t work if you’re trying to litter train him, it will confuse him. So for now, just leave it bare

Just as a side note, you said you put him in the pen… could you move the cage into the pen permanently and leave the cage door open? He’d have a lot more space and he could come and go as he pleases.

Plastic bottom cages are usually just temporary anyways… Buns outgrow them quickly. I second the suggestion to use the pen as an addition to the cage for increased space.

You are absolutely correct that having bedding everywhere encourages them to potty everywhere. A bare floor helps him to distinguish the living space from the litter box.

My bun’s home also has a plastic bottom. I also have an edible hay mat thingie that I put down because I thought he’d be uncomfortable on the plastic, but he still prefers to lay on the sides, where the plastic is. I think it’s perfectly fine.

You can attach the ends of the xpen to the bars on the cage. Zipties would work, or if you want the pen to be easily removable, you can use those big black binder clips, or “dog leash” clips.