Storing in proximity to where you are going to be using them is great advice. As well as planning your path of travel carefully too. Level or slightly downhill is great. Even small obstructions can (like a root mentioned above) can cause a big headache when moving a round by hand. Be careful, a round can get away from you on a steeper grade and cause a lot of damage.
Moving from point A to point B can easily be done by bumping along with your car/truck bumper if it can’t be rolled. Use winches and ropes with caution, they do break and can seriously injure anything nearby.
The dryer the hay, and the tighter your farmer wraps the round, the easier it will roll. Net wrapped is the best if you can find it. If possible avoid buying rounds that look like a tire going flat, it can indicate wet hay in the middle and it seriously ups the difficulty factor.
A dolly has always been interesting to me as well, though my ground isn’t level enough to make it much easier I don’t think (roots and rocks and ruts). And, bear in mind, you’ll need to find a way to get the round up on the dolly. I try to keep my rounds on pallets when I store them, try being the operative word. If the bale isn’t wrapped great or perfectly round, I can’t heft it up the 4 inches on to a pallet by myself. If you have two people its a lot easier.
I personally store rounds and peel off servings daily, but I only have two extremely easy keeping horses.