I think you could scan along the wavy curve, and convert the angle to a cylindrical coordinate.
Assuming the ribbon is the same length as the wavy curve, the x value would stay the same.
The corresponding y value would convert to a cylindrical angle.
The radius of the cylinder would be the half width of the ribbon.
The result would be curve on a cylinder. A sweep of a bidirectional line segment from the origin to the cylinder curve, would be the twisted ribbon. Fatten it...

I vaguely recall doing a "scan" a few years ago, in a script.

- Brian