This is a neat way of getting that big-roll feel, whilst preventing Crumpled Bill Syndrome, curse of the cash-short Maker.
Step 1: Materials:
> A rectangular piece of fabric. The exact dimensions depend on the fabric and your dowel. It should be as long as a typical bill, plus about half an inch, plus three times the diameter of the dowel. If you are using a fray-proof fabric, such as felt or tyvec, then the rectangle should be as tall as the length of the dowel. If the fabric is woven, and prone to unravelling, then add half an inch to the width for hems.
> Glue to match your materials. PVA will glue most fabrics to wood.
> About an inch of elastic (colour to suit your fabric if possible).
Step 2: Hems
Fold one narrow edge over by about half an inch and glue it down.
Fold both long edges over by about quarter of an inch and glue them down.
Leave your fabric under something flat and heavy until the glue is dry.
Step 3: Onto the Roll
Glue all over the dowel, and roll the fabric tightly around it at the end without a hem, just far enough to cover the dowel.
Leave it to dry, possibly wrapped in lots of rubber bands to keep it in place.