We use Tots Bots. You could send a wet bag into nursery for them to put the used reusable nappies into. But it would depend on the policy of the nursery if they are willing to use reusables.
I worked in a nursery before I got pregnant and we had a child in reusable nappies. Mum would send in a wet bag for us to store the soiled/wet nappies in until he went home. We removed as much of the soiled nappy as we could and then popped it in to a nappy bag and then straight in to his wet bag. It was never a problem for us in nursery however sometimes we would run out of liners for the nappy so we had to put a disposable one on him x
Personally don't use them but I would assume they would put the reusable ones in a nappy bag in there bag x