Vogue Knitting recommends the Alternate Cable Cast On for k1 p1 ribbing, and this is the bind off they recommend for k1 p1 ribbing:
Cut the yarn three times the width of the ribbing. Insert a yarn needle purlwise into the first (knit) stitch. Pull the yarn through. With the yarn needle behind the knt stitch, insert it knitwise into the purl stitch as shown. Pull the yarn through.
*With the yarn needle, sleep the first knit stitch knitwise and then insert the yarn needle into the next stitch purlwise as shown. Pull the yarn through.
With the yarn needle, slip the first stitch purlwise. Go behind the knit stitch and insert the yarn needle knitwise into the next purl stitch as shown. Pull the yarn through. Repeat from the * in step 2 until all the stitches are bound off.
Not sure if that helps at all. Good luck!