This VERY SHORT video tells what mice eat.... which is just about everything. Maybe if you continue to see droppings around your bin, you might put mouse traps out and/or cover the openings with screen.

All of my worms are outdoors .. some in a large pit, others in bins. I haven't notice droppings or [EEEEK!] seen any mice around them.

Here is a link that might be useful: what do mice eat?

borderbarb: thanks for the link.
It's only that 1 time so far.

You should put some mouse traps (humane ones preferably) and try to catch them.

what is a HUMANE trap?

For my money it's a trap that kills quickly and completely! (But that's just me.)

Generally it's one that merely traps the animal, but does not harm it in any way.

Here is a link that might be useful: A real example humane rodent trap

How about this mousetrap?
It will send you a text message when it catches a mouse, telling you the mouse it dead.

Here is a link that might be useful: RADAR Mousetrap

Funny you should mention this. I opened my worm bin last week and found a nest in the corner with a baby in it and the momma mouse.. I sicked the cat on that mouse pronto. She got the mouse and promptly killed it. I got rid of the nest and baby and set a trap. so far I have killed 3 of those rodents. We live in the country and I think they love that bin. It is made of wood and if there is a crack, they can get in. I keep traps set all the time now. So hopefully that will be the end of Micky and gang..

I forgot to knock on wood, when I posted earlier. Have discovered either a large mouse or small rat has been living in/around my worm pit. GROSS !! I'm putting traps and poison out and encircling the pit with dog feces. Hope that tripple whammy does the trick. [BTW .. am very careful with poison so won't hurt worms or expose my pets]

I thought mice had chewed through the plywood covering my outdoor bin until today. A large wood rat bolted out when I opened it up. It was 11/2- 2 lbs.... Time for a new lid, area clean-up, and traps!!!!!!!

Oh, dang .... Pete....I just finished posting a question to you on the critter issue on another thread. My pit is open top [cover with carpeting] Can't think of a way to keep critters out. If it becomes too much of a problem I may have to get my son to build me a real bin/pit. YUCK! Starting to sound like WORK.