OK, now I get it. Duh...
In the project Bill mentioned I used moire silk, which is rather heavy, so it wrinked beautifully. A fine, supple fabric may not work so well. I'm not sure batting would be of much use, either.
In order to ripple/rumple/wrinkle an appropriate background fabric, I suggest using a solid backing board of fluted polypropylene (aka Coroplast). Where you want the fabric to be not flat, apply lines of double-sided tape to the board, then bunch-up and stick the fabric to it as you like. To change the wrinkle pattern, lift the fabric and re-stick it where you want it.
If you use ATG for this, it would probably migrate through a thin fabric. I suggest using a tape with a carrier and good acrylic, non-migrating adhesive, such as 3M 889 or the equal sold by ASAP Tapes.
Another alternative might be to use an alphacellulose backing board; maybe 8-ply, or 4-ply reinforced by Coroplast or foam center board. Paint the whole front surface with acrylic medium or gel and let it dry. Then, lay on the fabric and fix the wrinkles by activating the acrylic medium as an adhesive using a tacking iron. I have not actually tried this method, so you might want to try it on a scrap first.