Hi Lucy,
Laminating your fabric is fine. Make sure that if you trim away excess plastic, you trim close to the edge of the fabric, but not right on it. You want to make sure you still have a sealed edge, otherwise, resin will leak in and stain your fabric.
A couple of tips to avoid the air bubbles:
1. Slide the piece in the resin on an angle. If you push it straight down, you are more likely to trap bubbles.
2. Dip your laminated piece in resin first. Something about surface tension (not sure the physics of this), but it will help prevent trapping bubbles.
3. Make sure your resin is bubble free before putting in the fabric.
Good luck!