a review of adhesives used by actual scrappers...and a lot more!
Most ways of adhering fabric would be with non-traditional adhesives. However, I have listed a couple of adhesives that would work.
1. Making Memories Ribbon Glue-this adhesive does not seep through ribbon, making a good choice for fabric
2. Xyron 150 or Cheetah-if you can get the fabric into the 150 or can hold it while you apply adhesive, these would be good choices.
Other options-stitch, staples, brads, eyelets