I use the EZ
Scooter Basket Liner. It has a zipper pouch, and two mesh pockets to hold drinks or cell phone. It is long from top-to-bottom so you can keep it open (as shown in product link below) or close it with the adjustable drawstring. Not sure if it is guaranteed waterproof in case of rain, but it is heavy nylon material. I would buy a cheap poncho to cover the basket and scooter tiller in case of rain, or plastic shopping bags. Have a few ponchos handy for the scooter user, too.
I use a scooter full-time and have taken it to WDW many times. There isn't any particular way to secure the liner to the basket, and frankly, I have never heard of anyone making off with a scooter basket liner. Ever. However, for your peace of mind, go to
Walmart and get the little 4" cable ties. You could run the cable tie through the mesh basket, then make 2 small holes in the liner to complete a closed loop. Trim off the excess cable tie.
I give you this link because they had the best price for the scooter basket liner. Their shipping was calculated to be $7.80 to my address. This site is a known disability supplier, not a fly-by-night. You can also search for your own supplier. Best of luck!
http://www.edmond-wheelchair.com/Me...n=PROD&Store_Code=EWRS&Product_Code=320000031