You can use strips of PUL or other poly or nylon fabrics to bind edges, just as you would using bias tape. If using a knit fabric, cut the strips across the width of the fabric (so it stretches if you pull on the ends of the strip). If using a woven fabric (coated or ripstop nylon, etc.), cut on the bias so that the strips have a bit of give to them.
She will want to use the 2-step application method - sew the strip to the outside of the cover, matching the raw edges. Then apply the elastic to the seam allowances. Then fold the binding strip over the raw edges of the cover, and stitch into place like you would bias binding.