Columbia's ribbon band on her hat makes it easy to disguise where the fabric from the brim and the topmeet. I use 1" wide black grosgrain (ribbed) ribbon. Pre-measure a piece to go around the base with a 1" overlap, spray adhesive on one side of the ribbon and apply the ribbon to the hat (figure 1). The spray adhesive is forgiving if you need to reposition as you work your way around. You'll want the ribbon to be fairly snug to prevent any gapping that the hat's shape or layers of fabric may create. Your overlap should be in middle of the left side (wearer's perspective) and the bow will cover the overlap.
The bow is a 10" piece of ribbon folded over and 'pinched' in the middle. Stitch a 1" line near the edge of the pinch to keep the overlapped ends together and create the bow shape (figure 3).
Take another strip of ribbon about 2-1/2" long, fold in half and sew 7/8" from the folded edge. This will be bow's "knot". Slide the pinched ribbon through the loop you just made with the knots seam to the back (figure 4). You'll probably need to press your bow a little.
Position your bow over the hand band's overlap on the left side and glue or sew in place.