I'm getting the impression that some of the responses assume you have a washable faux suede. Is that the case? And if so, is it pieced, or just one large area? If pieced and washable, you could use the temporary adhesive and stitch in the ditch to keep it attached and lined up permanently with the batting and back.

To answer your question, there are fusible battings available that fuse on one side or both. I found them via Google but have not tried either. I have enough of a challenge when I use spray fuse, which is repositionable.

I should clarify. my brain isn't working today. the basting spray doesn't make the quilt stiff to me. the fusible batting can do it temporarily. sorry.

Fusible battings still need to be quilted, the fusible washes away. If you don’t want to do very much quilting I would recommend fleece - it won’t separate or migrated with less quilting.

For your project, I would not use batting, I would use a well washed blanket so no quilting would be needed. If you are using real suede, how will you keep it clean? If you are using faux suede, you can do the same and never put it in a dryer, and only wash it in a “big boy” washer at a laundromat, and hang it on a shower curtain rod (moveable type that is wedged up, not nailed, inside the shower stall) with the quilt folded in half for a few hours, then turn it over so each side gets time to dry without creases. Good luck with your project.

I tried fusible batting once and hated it. On a smallish table square, runner or placemats it would be okay though. Without seeing your tooled suede bed cover, I'll throw out a possibility. How about light weight polar fleece? I have used it for wall hangings and baby quilts. It functions both as a durable backing and a batting wouldn't be necessary. It should adhere naturally to the back of the suede top without need for pinning, etc.

How are you attaching the top? Will you only do a bit of stitching or none? If so, I would probably quilt the backing and batting in a simple design and then attach the top. This would hold the rest together without requiring stitching thru the suede or ironing it heavily to fuse. But, it would make it more like a duvet cover than a quilt.

I found fusible batting (used on a small project) a pain in the behind. It seems more troublesome than just pinning and quilting as necessary. Doing it on a piece of tooled suede seems kind of chancy. Why not try it on a very small sample piece of the suede and see what happens?