My guess is the new bun doesn’t feel secure in his new home. This is normal for rabbits. A rabbit that feels threatened will either run and hide, or attack the threat. A new bun is often very cautious in a new environment so as not to draw too much attention to itself, until it gains so much confidence that it dares try to defend itself against perceived threats. Your bun is now defending himself against what he considers threats -the humans and the other pets. It is not a bad thing per se, it means he has healthy rabbit sass, but you should take great care not to “reward” his aggressive behaviour, because that will reinforce the behaviour. If you let him “chase you away” when he bites, it teaches him that biting works. Stand your ground (wear boots and gloves if needed, but do NOT punish him. This is something you can do yourself, but your dog and cat cant understand this. The risk is one of them snaps and lashes out, so you should separate the bun and the other pets at least for the time being, then later do a proper, gradual reintroduction.

Can you make an enclosure for the bun, one that only he has access to? It should have a hidey house, (an upside down cardboard house with two door holes cut out will work fine), preferably a tunnel (there are cat tunnels that aren’t pricey), his litterbox with hay in it and a water bowl or bottle depending on his preference.

If he gets a private enclosure he will feel a lot more in control of his environment and gradually get used to all the noises and scents in his new home. It will also help him form good litterbox habits. Most if not all rabbits need to be in a limited area during their first few weeks in a new place. Not a tiny area like a standard bunny cage, but an area that’s all their own.

How old is your bun?

Bam is correct. It sounds like this new bunny is overwhelmed with his new environment. When a new bunny is brought home, it is best to keep them in a smaller area like a room or an xpen and limit their interactions with other animals in the house. Let them get used to the sights and smells and, of course, you (the bringer of food and good things). Once they have had time to adjust, then you can start safe (controlled) introductions with the other animals. If all goes well, then the bunny can be allowed more freedom to explore.