Gwen Marston has a wonderful way to make binding. She takes a length of bias about 3 times wider than the result you want. Fold it in thirds so one edge covers the other on the back. In other words, dont but the edges.
Lay the ironed binding on the quilt and pin where you want it easing it around curves with an iron tip. So now it is all ironed and pined. Sew down the middle with a long machine basting stitch. Dont worry about color or how exact this is but just down the middle.
Now the binding is attached to the background and you can then do either hand or machine stitching any way you want around the edges (and they are turned under). When done, remove the basting stitches.
I have done this and it is so easy. Stays in place and the pins can be removed.