We keep bedding in the closet of the room where it goes. For towels I have a dresser in an extra room downstairs where extra towels are kept but honestly my kids have monogrammed towels from pbk and when they come fresh from the dryer we just hang them on their hooks on the bathroom door. Same for my towels and my H’s. So the extra towels really never get used.
It sounds like many of you have just 2 sets of sheets per bed - what's on the bed and an alternate. Do you have seasonal, as well?
I have flannel sheets for winter, at least 2 sets, and cotton sheets for summer, at least 2 sets. (I like pretty sheets.)
We have 2 sets of sheets for the each kids beds except for at Christmas time and then everyone has fun holiday bedding because we needed the cheer last year. I just stored it all with the Christmas decor (first in a vacuum sealed bag) in a Rubbermaid tub.