Did you manage to get a look at what sort of mouse it was? silly question I know but there you go. We get mice around quite often. Mainly field mice which are just crossing territory between fields / looking for somewhere warm to stay. They are not dirty animals, and if you are in the countryside, I would just prevent them accessing a food source and leave them to it, they can be interesting animals.
If you live in a town or city area though then it's a different matter, because obviously they are not on a natural diet and have more than likely been eating rubbish from bins.
First things first would be to cover all possible food sources, so if you have a compost heap for your scraps, make sure the lid is tight fitting. Put the rabbits food and hay in sealed plastic containers. Make sure all bins of any kind are closed and the lid weighed down. Sweep up all rubbish, dead leaves and vegetation (they like to use dry leaves and grass in their nests)
If you find any holes then block them off with super fine welded metal mesh or heavy bricks to stop them getting in the shed and going after food in the rabbits bowls.
There is no point in trapping them without doing those things, otherwise more will just move in. You could put down humane traps as another preventative in the future, just remember to check them regularly.
