Hi there,
Sorry things are not going as you expected, but the good news is I think with a few adjustments you will be much happier and it will feel less like you are living in a bunny litter box.
Bunnies need appropriate housing to make things go smoothly and safely for everyone, and I think some improvements to housing will help a lot of your problems. Having full and immediate free-roam doesn’t work for everyone, and it often isn’t the best way to start with a new bunny. Bunnies can be 100% happy and fulfilled without being 24/7 free-roam.
I would recommend getting an x-pen (puppy play pen made out of metal), and setting up your bunnies’ home base there (litter box, water bowl, hay, a hide, toys, etc). When he has exercise time, you can use open the pen and let him exercise in your room while you are there to supervise and prevent chewing. You can use a second x-pen to block access to your bed (or you might be able to use the same one, depending on how your room is set up. I would aim for 4-6 hours of exercise time, if you can. So that could be a couple hours in the morning, and then several hours in the evening.
It will also be important for you to bunny-proof your room. There is a detailed list tips on this here:
https://binkybunny.com/infocategory/bunny-proofing/
(There is also a ton of great info on housing, litter training, etc under the Rabbit Info tab at the top of the page)
There are lots of ways to set up litter boxes to make things more tidy. What is the current set up like? Using a screen (either metal or made of knitting mesh) can really help keep the litter from getting kicked out of the box and prevents digging. There are is a thread here where lots of different options are shown:
Detailed description of litter tray preparation
Rabbit makes a mess of his litterbox!!!
The other main thing is that you should plan to neuter your bunny. Litter box habits are often pretty bad until bunnies are neutered, so he might need to be in a more restricted area until that time. Litter box habits are also usually really bad when you first bring a bun home, as they are marking their new territory. It’s usually recommended to keep a new bunny confined to a pen for at least a couple days to let them get organized and improve their litter box habits.
Neutering will help with marking and lots of other hormonal behaviors. As he grows up and his hormones settle (and you dial in your bunny proofing), you will probably be able to give him more and more unsupervised free-roam time.
Bunnies rest and sleep many hours a day, just like we do. So don’t feel like you need to be in there 24/7. I do think that most bunnies are happier bonded, but they can be quite happy alone as well, so long as you spend time with them each day. Bonding is also something to think about farther down the road anyway, no need to rush into it. Bunnies are most active morning and evening, so spending time with him then is best (and also timing his exercise time for then is best).
If all of that still seems overwhelming, then rehoming may be the best option. But to me it is clear you love him, and by giving free-roam to start you are doing better than many.
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The answers provided in this discussion are for general guideline purposes only. The information is not intended to diagnose or treat your pet. Seek the advice of your veterinarian or a qualified behaviorist.