I use the cable ties/zip ties on one side as hinges and I use couple of medium sized binder clips on the other side to keep the door shut. They are strong enough so the bunny can’t push the door open. My rabbit stays in a 3 grid by 3 grid home with 3 levels during the day. He can jump up to the second level and has a ramp to the third. He has a place to hide on the first level, along with his litter box and hay basket. He seems to enjoy his basket and towel on the top level and spends his resting/sleeping time in the basket.

My rabbit chews on the rubber coverings over the bottom of the legs of my keyboard stand and piano stool. I had to remove the protective rubber coverings from them when possible, and otherwise put plastic tape over them, which he won’t chew.

Since you don’t want to risk her chewing a hole in your bike wheels when you leave her alone in the room, you should probably either figure out someplace else you can store it, or surround it in a gate of nic grids that your bunny can’t jump over while it’s not in use.

For latching the doors, you can purchase a package of very cheap dog leash clips that work very well.