The majority of my stash has been in under bed storage tubs - but not under a bed. There were 5 of them, stacked one on top of another, in a closet. They were preferable to deep storage tubs - at least fabrics were only one layer deep!
I decided to to move it all into a cube style storage unit from Target, which fits in the closet where the bins were. It took me two days of unfolding, smoothing or ironing (only when necessary - it's almost 90 here!) and refolding to fit the cubes. When I look at the picture, that seems like a ridiculous amount of time.
Next is to refold and organize fat quarters, then cut scraps into squares and strips. I only need another two days!