I ask for a bolt and wrap it on that. I have a spot in my cabinet where I left the shelves spaced out far enough that I can put an entire bolt in there, standing up. That's where all my larger pieces of fabric go, my wide muslin stash, and also my rolls of stabilizer and interfacing and fusible web stand up in there.
There are a few colors that I buy by the bolt so I made full-size bolt storage a priority when designing my cabinet layout.