Our first attempt at storing hay outside was a complete disaster.
We put a layer of pallets on the ground, then stacked the bales, then tarped over the top and tied down all round.
The tarps we used were not heavy duty - total waste of time.
As the tarps weren't tied taut enough we got sagggy pockets of water, which then seeped into the stack.
We didn't separate the tarp from the top of the stack - definitely should have had another layer of pallets or something.
We ended up with 80 piles of rotting, soggy hay with, I'm sure, some new species of fungus
We split the bales up and have spread them along the edge of the field - 2 years later they are still rotting down.....
I would recommend investing in a decent tarp and allow lots of air flow around the stack.
Good luck