The problem was that the bag was a tad small and since it was old, was already ripped and threadbare.
I looked around for replacement nylon but settled instead on a cheap doona cover I bought in an Op shop.
Quality cotton. Sturdily sewn seams. Flashy colours.
Extra hardware: Light bungee cord to wrap around the package.
Hand luggage for Mr Cool.
My last major outing 'into town' has convinced me that bagging is the way to go. I got on a train that was packed -- standing room only -- and if I hadn't folded and bagged the scooter I would have been a cause for much inconvenience and annoyance -- maybe even an injury -- in the carriage. As it was I could posed as a tourist and stood the package upright and lent it against my standing frame. So I took up not much room at all as we all stood cheek to jowl.
The doona cover scrunches or folds up into a dense little haberdashery fold when not in use -- which I can then backpack or lash to the handlebars. The wide mouth for the doona opening makes it easy to slip in the scooter and while the drapes are aplenty for now I'll see how much of all that extra I need for wrap around before I snip snip.