But correct me if im wrong but isnt one of the the things we get out bunnies vaccinated for carried by birds and mice?? i may be wrong on this one.
The mouse itself wont do much harm to the bunny, but mice can carry fleas. Which as Alpha pointed out, we get our bunnies vaccinated for VHD and myxomatosis, which can be spread by fleas, via the moving mouse. If it was me, id get rid asap, as even if your bunnies are vaccinated it isnt 100% safe, there have been a few cases on here of bunnies catching myxamatosis even though they were vaccinated!
We have our bunnies in cages and runs that are kept in a shed throughout the year, although there is a slight gap on the door as it opens inwards, so some mice get into the shed. Theres only been one occasion where a mouse has got into our bunnies actual cage, and this cage was high off the ground, with nothing i thought a mouse could climb up, clearly i was wrong! My bunny mustnt have liked it, as her food bowl (heavy, cermamic one) was tipped up over the mouse, what a shock i got when i lifted the bowl up! Another time we found a mouse in the bin in the shed, by the time my dad got home to get rid of it, the mouse had had a litter of babies and ate some.
We use humane traps which for us work aslong as we make sure there isnt anything nearby that would appeal to the mouse to eat. We always sweep the floor, keep the bunnies clean, and keep food and hay tidy and safe, and as high up as possible. We mostly get them during winter. I once had a mouse jump out of a bag of hay, scared the s*** out of me, so now im always a little wary! Rabbits will always attract mice, thats a fact, you just need to help minimise the risk in my opinion.