I hope that you all see this post as I'm jumping up and down saying "I know I know I know - pick me!!!" as I read your question!!! POLYESTER is the way to go when it comes to invisible thread ALL DAY LONG!!!
Superior Threads Mono-Poly is the one I use. It's wonderful. You CAN use it in the bobbin but I have much better luck using either a thin cotton or a regular polyester thread in the bobbin.
***BIG TIP - if your new to free motion quilting and using a polyester thread or polyester invisible, use a smaller needle. A 10 is usually what I use but even an 8 would be good for the thin poly. If you have tried it in the past and had problems the needle could be a big reason why - you can have loops, thread breaks, catching, skipped stitches...also you'll want to drop your tension down low. All machines are slightly different but my machine usually I set the top tension at a 0 to 1.