Welcome!

So, I have to ask, is bedding necessary for a rabbit?

No, it’s not necessary. You can save money spent of that for something else.

To get he pooping in the box more, make sure it’s a decent size and that she can only access hay by getting in it. I think that will really help.

When I leave for school or work and come home, I notice some of the bedding has been pushed out of the way and the rabbit lays on the plastic of her cage.

That’s pretty common. They do seem to prefer a bare surface.

Because she is still young, I don’t think you have to worry about sore hocks just yet. (Weight and long nails can contribute to sore hocks).
It will be easier to instill good litter habits if the cage is bare for now. Then later, you could introduce something to protect her feet. Those memory foam bath mats might be suitable, but you will need to watch if she’s a chewer!

I own two destructo-bunnies. There is no way I can keep any fabric or non-edible foamy things inside the cage (except for the hay bag). However, I do put down sea grass mats, and that works really well. Like Jerseygirl said, I also keep their nails trimmed regularly.

I agree that bedding isn’t necessary, many rabbits just push it aside as yours does. Some do well with a folded fleece of memory foam mat as a soft resting area, but others don’t and are too inclined to chew.

Enjoy the savings

Olly pushes his blanket or old towel to the side and sort of cuddles it, if I put shredded paper bedding in his bed he thinks its to do tinkles.
He likes to take out his blanket sometimes and lay on the plastic of his cage or bed, so its normal.

When i got Charlie(4 months old) I quickly learned that putting any type of bedding down in his cage was a terrible idea because he would pee on/eat everything that looked soft and comfy so removed everything except the litterbox pellets. Then i started to let him out to run around my room and he would chew on my fuzzy carpet like crazy trying to destroy it and if he was not busy doing that he went and peed on it and it almost drove me crazy…

Its now a year later and i can gladly say that the issue is almost resolved. Although he stayed a bunny that dislikes soft bedding(he is still scratching off the flece from my couch when sometimes) he can now tolerate it better. He slowly lost interest in the carpet and he has a pillow wraped in a fleece blanket in his cage which he sometimes still gets angry on and chews a bit but does not pee on it. Most of his cage floor still needs to be bare and the pillow is just there just in case he would like something softer (mostly to just lean his head on it).

So i would say just wait it out and hopefully after she has gone trough bunny puberty she is going to get a bit better behaved and calmer.