I don't think I'd be overly concerned if mice got into our shed to be honest as they're not as germy as rats (allegedly). You've taken out the food tubs BUT you cannot remove all the food as you still feed the rabbits in there so there will be bits left behind that you can't do anything about. No matter how good your bunnies are at hoovering, there will be bits left behind and the mice will find them. Best thing to do is to try and find the entrance hole. It/they will be tiny, as small as the diameter of a pen or pencil, and block it up.
They may be after the hay for bedding for their own nests - they may just decide that the shed is a better, easier option for said nests!
Do not use traps or poison (obviously).
The only way you can stop them is to find out where they're getting in and block it.
Good luck!