Well, depending upon how thick the insulated bag is, I would use the double sided tape to tack it down and then reinforce the perimeter with painters tape...can never be too careful..
I'm so glad you asked this question and I see you have already gotten some good answers. too. Keep asking questions. That's how we all learn.
Scotch tape, double sided, is what I use. I am pleased with how easy it is to use. I have crippled hands.
SQ
Haven't done this before. I think I would try using as much masking tape everywhere possible (avoiding the stitching area) to hold it in place. First thought of paper clamps but I don't think these would hold firmly enough nor be easily kept out of the way to keep the embroidery arm moving freely. Good luck.