To obtain a nice stretchy bind off for K1, P1 circular ribbed items such as the tops of sock cuffs, we use a modified Kitchener bind off.
The modification is to omit some of the preparatory rows that you see in many instructions (these rows slip half the stitches for a couple of rounds and create a tubular finish). We don’t need the in-elasticity of the floats behind the slipped stitches.
Start by cutting the attached yarn to a length about 3 times the circumference of the item to be bound off. Place this yarn tail on a darning needle. Prepare by separating the knit stitches onto one needle and the purl stitches onto a second needle. It is helpful to move these onto a needle that is one size smaller than your working needles (this does not change the tension of your bind off, it just makes it easier to work the stitches with the darning needle).
First two stitches (preparation): Bring the yarn through the first stitch on the front needle as if to knit and slip the stitch off the needle. Bring the yarn through the next stitch on the front needle as if to purl and leave the stitch on the needle.
Step 1 – Back needle. Bring the yarn through the first stitch on the back needle as if to purl and slip the stitch off the needle. Bring the yarn through the next stitch on the back needle as if to knit and leave the stitch on the needle.
Step 2 – Front needle. Bring the yarn through the first stitch on the front needle as if to knit and slip the stitch off the needle. Bring the yarn through the next st on the front needle as if to purl and leave the stitch on the needle.
Repeat steps 1 and 2 until all stitches have been worked off.