I don't think he needs time to himself, just his own space. He probably loves you -- a lot -- and is territorial and jealous of the cats.
And he's still in the bunny-from-h*ell age. It does last awhile.
Pipp, my bonded mate, was the sweetest rabbit until her terrible teens. It took a few months after her spay for the hormones to calm down her to get back to her kissy-bunny self. Part of the process involved blocking her into my room instead of giving her the run of the house, as noted -- she was exhausting herself.
She definitely prefers just living in the one room, she has no interest in leaving, at least not as long as she just convinces herself she's the only bunny in the world. But even now she'll still try and maim any cats brave enough to try and come into OUR room.
My heart bunny Dill was an opinionated biter, he'd nip me if I missed behaved -- Dill loved me, but I had to behave -- and I loved every chomp. They really don't do much damage. And it was just a disciplinary thing, it wasn't hate or anger, just his version of the water pistol. (Hard to work one without a thumb).
I'd really recommend getting your bunny a bunny friend to take the pressure off you as his mate. Neither Dill bonding with Sherry nor Mister bonding with Darry made either any less friendly towards me, they became calmer and less obsessed, but just as pet-able.
Mind you, in Dill's case it didn't help the cats much. He and Sherry started ambushing them in tandem.
But it was all in good fun, just a chase game. The cats figured it out.
And for the record, Darry was a snotty, ill-tempered
bunny when she came here, and the only one (aside from Scooter-the-Monty-Python bunny) who ever intentionally drew blood. She lived in the back with Radar for four years and moved into the living room to live with her new mate, Mister, when Radar died a few months back. And lo-and-behold, with just a few months of daily up-close-and-personal human time, she's turned into a very friendly little rabbit! There's hope for everybunny.
But you really won't have to worry about him if you get him a mate. They're very content with a bunny friend and a little space.
sas :bunnydance: