To neaten the handles of the bag sew a narrow hem as close as you can to the edge. If you have a rolled hem foot on your machine you can use this here. Otherwise, fold over just under a centimetre and then slide your nail under the fold to tuck in half of the hem allowance. Don’t pin first! This allows the fabric to find its own way to sit and a very narrow hem can be created.
You could always use bias binding to neaten the edges too. Try following the Visible Binding tutorial.
Then press everything as flat as you can.
Thread the piece of ribbon through the casing and tie a knot.
You can use your bag whenever you need to and then fold it all up again into it’s own little pocket.