I do NOT feed round bales mostly because how my property set up (just no space to keep them plus I have just 2 picky horses who throw too much hay around). But from what I was told by hay person the best way to go is to keep them on wooden racks (I use similar in my sheds for the square bales) and cover them with tarp. Also if you feed round bales it's a really good idea to give a botulism shot (that's a suggestion from several horse people and 2 vets I talked too).
My hay guy doesn't keep the hay - whether you pay him or not (I asked). You get it or loose it. Lol! So I try to buy everything before Jan (got bales just before NY).