We’ve had mice twice since moving to the country. i know the feeling-your so worried about potential harm to the bunnies.
Here is my thinking….
Mice are everywhere-they live in (re; poop, pee and eat) in the fields where your hay is grown….where the hay used for pellets is grown. If there was some potential to cause disease, we’d all have that disease in our bunnies.
I think should you have an illness in the next year, you mention to your vet you had mice -so they can take that into account if it applies. But honestly mice are peeing and pooping and eating the food supply so I don’t feel it could possibly be a risk. Additionally in England bunnies often live outside and quite a few members have posted pictures of mice eating with the bunny.
I would suggest not using poison-they can die in the walls of your house, or be eaten by cats or dogs and kill them too. If your going to use live traps, ensure they can’t admit more than one mouse as they will fight and it could be a while before you find them. I prefer the snap traps-they are quick and don’t pose a risk to anyone else in my house. Peanut butter works great.
Now the most important thing-you must go inspect your house for how they got in. It can be the size of a dime. It could be on a vertical wall or the roof. Call a professional if you need to. If you don’t find where they came in and seal it, they will be back.
Good luck!!