I have many floral displays that we switch out at the cemetery. I am looking for a way to store them so the arrangements do not get flattened or misshaped.
You can use cleaned, empty oatmeal tubs if the bouquets fit. Push the stem end through a small hole poked in the lid, and they'll hang upside down without touching the sides of the tub. If you don't think you managed to get the tub quite clean enough, you can line it with a produce bag from the supermarket.
If they're too big for oatmeal tubs, try empty shoeboxes - you might be able to fit two bouquets in if you put their narrow ends on oposite sides of the box.
A possibility for short, round bouquets is 2-quart food containers, either something like recycled margarine tubs, or ones you purchased just for storage.