My longarmer and I have successfully bartered services (my computer services for her longarming a show quilt), but we are very good friends and, because we are both quilters and both computer geeks, we each knew when the balance had been reached. No rates were ever mentioned, nothing was written down, and we are still very good friends.
Your situation is very different. If you go the "rate" route, you should come up with an honest hourly rate that covers everything, materials excluded, for a custom quilt, start to finish. You shouldn't have to break it down or explain how you came up with it, and you certainly shouldn't involve her in determining the rate. It's the rate for
your work and you do not have to justify it any more than the trainer has to justify her rate to you. It shouldn't be any more negotiable than your plumber's rate. Materials would be a separate expense and she can decide whether she wants to purchase them or reimburse you for doing so (time and cost).
If you go the "time" route, the trainer will likely decline, for surely it takes you longer to make a quilt, especially if you have to shop for the materials, than she would be willing to match in lost training revenue (if she's training you for free, she's not training someone else for pay). Average personal trainer fees are in the $30-$60/hour range at a chain gym, $50-$100/hour if private, so, in reality, her time probably would be worth more than yours.
Be very, very careful. There's not much worse than a barter arrangement gone sour.