I watched "How to bind a quilt without binding", which is turning your backing to the front. I've done that numerous times and have good luck with it.
Two things I do differently: I cut the baking more than an inch from the edge of the quilt top. An inch and a quarter or a little more will do. Then fold the back over as she does, but tuck that extra under the batt. That way the edge is always a double layer of fabric.
The last one I did, I mitered the corners by folding the entire quilt on the diagonal so that two sides are raw edges together. I sew from the corner of the top out to the fold line, just as far as the width of the binding will be. Then the corner fabric can be trimmed away, When you turn that right side out, it makes a perfect miter. Tuck excess fabric under and you have a perfect corner.