Another option might be to store them in different areas - get an armoire/linen press for the bedroom and then store a few everyday bags in the closet itself. Get doors!
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http://www.organize.com/parkapurse.html
I have these in both closets...helps a little bit...but I need a better long term solution!
Off to search for the thread Swanky was mentioning!
Maybe Swanky can post the search terms, because I can't find any good threads on this either. I found these by looking for "storage".
Do You Stuff
Do You Store your bags in dust bags
Storage
OMG I think I lost a bag
Cedar Chest OK for storage?
Do I Store it in the box too?
How Many
Storage in an IKEA PAX wardrobe