I think the bugs will go away once the wood is dry. I'm not sure if that Shelter Logic cover lets the wood dry as fast as the sun and wind do. Ants like to build in my piles too but they tend to go away in the winter when I need the wood. This is one reason my wood piles are a long ways from the house until they are dry (2+ years). In the fall I move it up to the house (but still outside) and bring wood in as I need it.
So I guess to answer your question, I don't know of a way to get rid of them. I'd just let them poke holes in the wood to help it dry
Edit to add: Looks like your pile may be in the shade. Moving it into a more sunny spot could help. And one crazy way to keep ants out would be to elevate your pile above the grass (8" or so) and put water moats around the legs of your wood rack so the ants can't climb up into it.