Erm....well I am not too sure about this.
I am not sure that mice are "awful" in the sense of their carriage of.......stuff lol, not sure how to put this. So I am not sure they could potentially harm the buns, although don't quote me on this.
We live right opposite a farm, so we have had amouse in our living room when I was about 10, and then we had another mouse outside. We used humane mouse catchers which were great. We then took the mice and drove down a few miles and released them into a wood, so that they could not come back.
Twice I have gone outside and seen a mouse sitting on top of the hutches, happy as can be, and once inside the wheelie bin I keep full of hay by the hutches; he had made himself a nice little nest in there!! And then he jumped at my face and scared the bejesus out of me- it was dark outside and something leaped at my face!!!
I've tried everything I can to block the mice from my buns- checked the wholehutches over and made sure there are no "entrances". I have put a brick on the lid of the wheelie bin of hay to make sure they cannot get in there, and my hutches have removable "windows" my Dad made so the rabbits keep warm in the winter and it keeps the rain out- so this would help prevent the mice from getting close to the buns.
Apart from doing something like that, making sure you prevent the mice from going into the rabbits hutches etc. and keeping food in a tight tupperware box or something similar. I am sure it will be fine though.
Good luck
Anyone who has any other thoughts on this might be more helpful than I have been, but I hope I have helped a little.
Jen