How much do you need to add to get to the edge of the bed? If it's not too much, I would add whatever border you want, then do a larger border of a tone on tone for the drape and then add another border that matches the first border along the bottom.
So, it would go: Top, main border fabric, drape border fabric, main border fabric.
You just have to make sure that the drape border starts exactly where it falls over the edge of the bed.
Watson