Use the weakest bleach water solution that will do the job. A water
rinse should get rid of the bleach. Most anything except mild soap and
water will affect the fabric and stitching. It must really suck to have
to put your toys in storage for the winter. ;-)
It's not just the winter. During the summer months it sits in the slip with the cover on it, and it builds enough moisture under that cover that it will start developing mildew spots. Those are easy, but the ones that develop during the SC winter are much worse.
I'll probably pull it out of the water this year for those four months where we don't use it much. Maybe that'll cut down on the moisture and mildew.
I could just leave it uncovered and let the sun and rain take it's toll. Probably no mildew, just would have that fresh "sun-baked" appearance after a while.
Does your cover have vents? Maybe that would help.
--
Guns don't cause problems.
Gun owner behavior causes problems.