I finally found a solution for how to store my gift wrap.
I previously tried a solid gift wrap holder make by a famous container maker. But it was bulky, did not stand up well, and was awkward to carry in the house or car.
This holder has 3 clear pockets so that it is easy to find the ribbon, cards, or tape that you want. There are Velcro straps which keep paper gift wrap rolls in place. It will also accommodate folded paper and bags. A zipper secures the organizer into one neat package which can be laid flat or stood on end for storage. There are two web handles for easy transport.
The organizer is made of wipe clean vinyl. It is made in festive green and red colors. For the price, I consider it to be very well constructed. It is similar to soft sided luggage in the way that you can always cram in more stuff if necessary.
I bought mine a couple of years ago and am very happy with the purchase. This is item number F1454 at Harriet Carter gifts, and recently they did seem to still have some in stock.