I presume these are bare root plants. I wouldn't use bleach. I would use diluted damp off the same as you would use in a pot of seedlings. Even though there was no frost there must have been dampness. I hope the mold hasn't killed the plant.

Another year you might think of a closed box with shreaded paper or something to keep the moisture away from your plants

Where do I find this damp off product you referred to?

You can buy it almost anywhere they sell fertilizer and plant products. It comes in a little bottle and costs somewhere around $2. You might want to let your fingers do the walking.

If you have an eye dropper it will help getting it into a watering can, but rinse it after you use it so you don't contaminate the Damp Off the next time you use it. I keep mine with an elastic band on the bottle. You mix the Damp Off with water and it kills mold. It is mostly used for seedlings and the fungal disease damp off but it will work on your plants too.

Any time you put a plant into an environment where dampness is about, then you can expect to see mold or mildew. Keep that in mind next time you store plants over winter. Cool, dry and dark is the best way to treat them.
They don't need water, they don't need light. Temperatures about 38º to 45º is good. Warmer and they might start rooting which you don't want.
If you haven't already, cut the plants back, remove all the old leaves and damaged or weak stems. Fresh potting soil, maybe mixed with some peat moss and coarse sand.
Put something on the bottom of the pot so that the soil doesn't clog up the drainage holes. Water to drainage.
Then take them to the sunniest window you have, but not a north facing one. Turn them every other day 1/4 turn.
Always water to drainage.
The sun will do the rest. After the first watering, no more water until leaves form in about a week or ten days.
Fertilize only when the plant has sufficient foliage to warrant the food and then at 1/2 rate until it goes outside later in April.
After watering, let the plant drain, then dump the excess.
Soon the plant will resume its old self and you can give it increased amounts of outside daylight as the days get longer and back inside at night.
That all there is to it.

Spray the mildew you see with a light solution of citric acid. (lemon juice and water)

I just wanted to add a question along the same lines if I could. I overwintered my Geraniums bare-root in a cool, dark closet in paper bags. I have brought them out, soaked them in water for a few hours and then potted them up in a good soil mix. They are sitting very close to growing lights, but not directly underneath. The watering has been kept to a minimum. It has been about 3 weeks now and no signs of life... except on one and it is weak. Was it all for naught? Is there anything I can do to encourage them to come back to life?
I did overwinter a number of Geraniums in pots in the same closet as well. These have all come back to life and are growing vigorously. Perhaps I should just stick to this method :)
Thanks for your help!