We always put fine gauge chicken wire underneath ours. It keeps the rodents out (they gain access by tunnelling underneath), but it still lets the fluids produced by the rotting veg run away and the worms in. You can buy a sort of stand thing for your bins that will collect the fluids which can then be used as a plant feed, but obviously this will prevent worm access so the whole process may take longer. We put our rabbit's poo in the compost bin - it's a great activator - so I suppose mouse droppings will be the same. Also their tunnelling activities may mean they're helping to mix the compost for you. I suppose it depends on how you feel about it all - personally I'm not a very rodent friendly person!