I don’t think the mites will hurt the violin, but you can put moth balls (a couple) in a pocket of your case and it will repel all critters. You’ll have a stinky moth ball smell, so this is ideal for storing a violin but if you want to preserve the case, you can try this. Also never put your case on the floor. Not even while keeping it closed, if you can help it. Somehow this makes it possible for the mites to get in the case easier.
Oh, and I would recommend loosening a bow between practices.
Here’s some more suggestions about the bugs that love to eat bow hair.