You can store it outdoors. If you can try to ensure it is just moist and fluffy and not soggy wet when storing. Being on the dry side is also good. If the bags do not have holes it will not get any more wet. If it is too wet then the freeze-thaw cycle through the winter will break down some of the bark. Wet peat will suffer more if it is soggy wet. So just moist and fluffy should be a good target. I keep mine outdoors (including bagged bark) outdoors under a tarp weighted down with stones/bricks.

I mix and store in the large plastic totes (30G) available at any box or home improvement store. The mix stays dry (more or less), fluffy and is always available for use as needed.