I started writing how I would put the bag together but lost my text after looking at the picture again on my iPad !
Use a 12" wedding ring template to cut out the fabric. sew four rings together in a row with out one melon on one of the side rings. Cut another center out and cut it in quarters. Sew a quarter to the bottom of each ring. Quilt the whole thing leaving an unquilted space 1/2" from the sides and bottom edges. Trim batting to back to the quilted edge. Sew the open side of the row to the melon ring on the opposite side. Turn bag inside out and sew the bottom quarters together to form a boxed bottom. Leave the backing out when sewing the rings and bottom together. Then hand stich the backing down.
I would put put in a lining and then bind it and add the handles.