Pill bugs like to eat decomposing cellulose, like in paper, cardboard, leaves, sawdust, etc. I don't think cornmeal will have any effect on them at all. I put a half dozen or so pill bugs in my bin hoping to get a population going, and they all eventually escaped and died on the floor.

Several years ago I had a bin in my garage. I had a large pill bug population in that bin. They overran the bin, but many of them also escaped.

My guess is that if what you have is pill bugs, they will contribute to the breaking down of your bedding until they all decide to escape. Pill bugs don't breed as often as worms, but they breed in large numbers when they do. If you still have pill bugs after 6 months or so, they will probably be permanent guests, and you will find dead pill bugs all over the floor.

"Bugs are very new, still white and tiny"
My guess is that you have mites rather than pill bugs, especially with an indoor bin. Also you mention moisture, and pill bugs don't like it tooo moist.
Do a search on the forum for mites- you'll find plenty of posts!