Version 2: Hand-Stitched
Start the same way you did for version 1: by cutting a bias strip of fabric 4x the width you want the final binding to be. For instance, I like 1/2" binding on my corsets so I cut 2" strips. My favorite way of doing this is with a rotary cutter, but employ your own favorite way of cutting continuous bias, there are a ton of ways out there. If your bias is not long enough for your edge piece strips together to get one long enough.
Place your bias tape on the edge you're going to finish with the right side down. Pin it in place with the edge flush to the raw edge of the fabric.
Sew the strip down. The width of your seam allowance will be the width of your final bias binding, in this case 1/2" seam allowance equals 1/2" bias binding.
Press open the seam you just made with all the seam allowance toward the bias tape side. Then fold the bias tape over and press again. Finally fold under the edge of the bias tape so that you have a clean fold on the inside and press. With this method it isn't important that the fold cover the seam.
Using a needle and thread slipstitch or blind hem the bias tape folded edge to the fabric. In the case of a corset with multiple layers try to hide the stitch length in the fold of the bias or between the two layers of fabric and be sure to only catch the inside layer with your stitch so that your stitches cannot be seen from the outside.