I cut, or usually tear, them into 1.5" strips and wrap the clothesline. Zigzag with about a 5mm wide stitch so that the swing will hit both of the cords.
Shape as you go by tilting the bowl. I use a glue stick that is washable and acid free (most are) to connect the strips. Important to remember. You need to coil and sew clockwise, left to right and make sure the right side of the fabric is showing when you wrap. I coil the fabric for about 6 inches and then place a pin to hold it in place while I zigzag.
This method can be used for coasters, bowls. wall hangings and bags. Just modify the shape and the size. I finish off mine with hand picked shells from the West Coast of Florida. I leave about a 6 inch length of the cord and glue it in the desired shape to the bowl with an industrial adhesive. When the glue is dry I use the same adhesive to attach the shell.