I live in Dayton, OH. I wonder if there are any feed stores that sell bales of timothy or oat hay in Dayton, columbus or Cincinnati? Hay sold in pet stores are too expensive indeed.
I go to a farm and pick up hay, they have a great veriety and quality. $7 for 60 pound bale of timothy or orchard and $10 for alfalfa. Now my kids won't eat pet store hay because it's not as fresh.
Being in Ohio you should have easy access to farms, just make sure the hay is horse quality. Try googling to see what is around you or even the phone book.
I spoke to one of my friends who's mom rides horses a lot. She got me a deal on the hay they have their (not alfalfa), and I pay $3 for a bail. Quite the bargain!
If you live in an apartment, do you have a storage unit in it? You could always put it in a big bin down there, and then have a little box you bring some up in at a time.
The bin should have holes drilled in it for ventilation. And after you remove some from the bin, flip some of the remaining hay over so the same part doesn't stay in the middle. And even this, if the bin in in a basement, might not be good enough to prevent mold.
So to be safe, the bin might be better off in the back of a closet.
I don't know about where you live but I get my hay at fleet farm they have 50 pound bales of really good quality Timothy hay for only $15!! It's a great deal my bale lasted for about 3 months and stayed fresh my two bunnies love it!