I decided to sew another line parallel to the first, again all around the opening. Then I made an opening between the lines, reinforced it with some hand-stitching, and used a safety pin to add the drawstring.
Also, I didn't like any of the ribbon that I had (that were the right width) for the drawstring, so I took a scrap of fabric and sewed my own. Finally, I added a bead to the drawstrings.