I just finished a quilt with QD cotton, select ? ( the second from the thinnest weight.) The back was very dark, and there is no bearding. However, the back was a blue/purple batik, prewashed, that bled just enough to destroy some of the colors on the much-lighter top. The batik was much more tightly woven than most quilting cottons, and the amount of bleeding on prewash seemed negligible. I'd explore using a batik back in more stable colors next time.
hugs,
charlotte