Actually, in your case I think you don't sew any more or less. If your binding is still 1/4" wide, then the unsewn section is still 1/4". What changes is the way you fold. You don't fold on a 45 degree for this corner - you need to match the corner you are binding. What I figured out when I did my table runner is to use the fabric itself as a guide. When you fold a 45, and then you fold the working end back down over it to continue sewing, notice that the left side of the 2 layers of folded fabric align precisely. Do this every time, and you can mitre any corner.
So, stop sewing 1/4" from the end. Fold up at the point you finished stiching, along a line that approximately splits your angle in half. Then fold back down, along the line of the edge of your piece. Now, holding on to the corner of that, fiddle the left edge to get the 2 layers of fabric to align. Then continue sewing as usual.
Wider binding I'm still learning. But I think you still stop sewing 1/4" from the edge (assuming you are using a 1/4" seam). Then, you fold up the full width of your binding (not just 1/4").