Answer: There is a way to overwinter geraniums that involves storing them upside down but not necessarily hanging them upside down. To overwinter geraniums bare root as you describe, they need to be dug from the ground before frost hits. Shake all of the soil from the roots, put a paper bag over the entire plant and store upside down (roots up, stems down) in a cool but not freezing, dry place (in a box in an unheated garage or crawl space is great).
In late March, plant the geranium in potting soil in a container big enough to accomodate the roots. Water thoroughly and place in a cool (45F) location that receives bright yet indirect light. As the stems sprout leaves, move into direct sun and apply an all purpose fertilizer such as Miracle Gro carefully following application instructions. Remove any dead stems before setting outside.
The above method only works if your storage area is "right" and finding it may take some experimenting. Unfortunately, it seems many modern homes do not have an area that is cool and dry enough. This is an old fashioned method that relies on a true "cellar".
Alternatively, you can treat them as houseplants for the winter if you have space. They require lots of sun and watering about once per week. Feel free to cut them back, since they'll send out new, tender growth and blooms. If you don't have room for them on a window sill, you could try putting them in dormant storage while still in pots.
To do that, gradually reduce watering, and when the foliage dies back, store them in a dim, cool (40-45F) basement or garage. Check them occasionally during the winter to make sure they don't dry out completely. When danger of hard frost has passed, repot, water, and place them outside.
After a year or two, your geraniums will become woody and produce fewer blooms - at that point, you can start new plants from cuttings.
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