Well i have my big barn obviously, but down at my sheep sheds i have a leanto which holds about 40. My leanto is sheltered on one side by a shed and tin sheets on the other side but open front and back. I always stack onto pallets. Its okay as long as the rain isnt blowing in.
As the horses are currently in the bottom field i have no hay storage so i drive down with enough bales to last the 6 days they are down there. It was 3 originally, then went to 4 as the grass went down, now its 5 bales. I just stack in the field. If its a wet week then the bales do get more soggy. However since chunky developed that copd symptom a couple of years ago and i had to start soaking it because of the cough im not to fussed if it gets a bit wet. This year it actually has worked in my favour and hes only had a few cough days. Think that was when we had a dry week funny enough. Im not deliberately having to soak it myself which was hard work. Neither of the boys are a fan of completely soaked hay. So the wades are part wet and dry.
How long is a round bale going to last you if you left it in the field. The one thing i did find last spring when out uncovered if i was taking out several bales, as the temp warmed up in spring and if it had got wet it started to get more mildew/fousty hay smell. Its seems okay at the moment leaving bales out several days as its cold.
The only dilemma you will have is if its raining and you have a cover or tarp over you get wet trying to uncover it. Not ideal on your flying visits before work.
You could use a plastic sheet and get one of those rachet/lorry straps. You can get the rachet done up tighter than having a long bale string going round the sheet and bale. That way it stops the wind whipping the sheet off. We tarped and racheted the large hestons in one field last year for the cattle.
If you can roll the bale onto a pallet to keep it off the ground that will also help but its not easy to roll them onto pallets.