Is her table runner an octagon? The 135º binding just means there are outside angles in the shape of the finished piece. I wouldn't cut the binding on the bias for anything that is not curved. You miter outside angles, or any angle for that matter, the same way you do 90º angles. The binding is made the same way as usual.
When you fold the binding up at the corner, you line it up with the next edge of the quilt, same way you do when it's 90º. Make sure the fold bisects the angle at the corner before you bring the binding back down. (I usually pin it.) The top fold will NOT bisect the angle, but it should hit right at the point of the angle. Stitch through both folds and continue on to the next corner.