The Mylar alone would be fine but make sure it really is Mylar-D and not just masquerading as such.  Don't tape the Mylar to the tube otherwise you'll just create another problem.  Most tape adhesives with eventually fail and leave residues. Use the the muslin as a dustcover wrapped around the outside of the textile or if you have enough mylar use that instead with ties closing the ends.  Mylar won't absorb dust and other particulates from the air, unlike the muslin.  If you choose to use the muslin you'll have to wash it periodically.

Michelle Gallagher, Collections Manager

Palm Springs Desert Museum