Use sturdy/firm fabric like denim or canvas. You could use a very firm interfacing between cotton layers if that works better for you. Otherwise, the bag will sag and items will fall out of pockets. Also, use washable plastic to form the bottom. If possible, use inserts to keep the bag shape on the top too. I'll look for the name of the product I use and add it here if I find it.
I hope this comment translates well or it is at least funny if it doesn't.
Thank you for your good ideas, I know which insert (inlay) you mean (in German Schabrackeneinlage) Thank you :-)
I have seen a YouTube on how to sew one - but, I haven't done it myself. Good luck!