Neat handlebar bag from Giant Loop.
This is about the size of a fanny pack but loops across the bar pad of your bike if you have one. You can of course strap this to lots of other spots on a moped or small moto. We've put these on the racks of Puch Maxis and Motobecanes.
We use one of these on our Yamaha DT50LC to carry a little bottle of oil, a rag, and a couple of tools. You can also stuff this thing full of snacks or just a pair of sunglasses and your ID.
Large single opening with a mesh zippered divider inside.