Hi there, welcome
So, there are so many strategies out there it can be overwhelming. A couple more questions will help me give some advise.
First, with shy buns, it can really help to do extra pre-bonding (cage swaps) along with a bit more settling-in time at home. How long after you brought the new bun home did you start sessions? And have you been doing any cage swaps? The idea is to make sure they get used to each other’s scent and to make sure the shy bun behaves pretty normally during bonding sessions. If you started bonding sessions immediately, I would pause and go back to doing cage swaps for a few weeks.
Second, neutral territory is probably the most important element for establishing a bond. I have a studio apartment, and had to get very creative with bonding space. My bathroom was OK, but I had the best luck with setting up a pen at a friend’s house in their garage. My local rescue would also let me bring them in to do sessions in their exercise pens.
Next, you will want to focus on building trust between them, so whenever the male approaches, pet them both a lot to swap their scents and make them think they are being groomed. Try to do this before nips happen.
It can honestly feel like progress isn’t being made, but your goal is to promote peaceful sessions. Any session where they don’t fight builds trust. So if that means petting the boy in her presence so he doesn’t bite her, that might be a good strategy.
In general, approaching with ears up and tail down = interest/curiosity, ears down, tail up = aggression. So if you see his ears go down when he approaches, be ready to pet and intervene.
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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.