...plastic shoebox with a lid (I purchased mine at The Container Store, www.containerstore.com, but you can also find inexpensive ones at the dollar store).
You also may consider storing them in different locations like the kitchen, closet, car, garage and anywhere else a bag might come in handy.
Repeat the steps 1-8 with the rest of your bags. If you have tons of bags you can always finish them while watching tv or doing some other activity.
(Also, if you truly have tons of bags that you may never use consider recycling them by donating or using one of the ideas found at WikiHow (http://m.wikihow.com/Recycle-Old-Plastic-Bags).