A practical padded bag that is designed to protect the saddle during travel or storage is the Horze Saddle Bag.
The sturdy lightweight material will keep dust off and allow you carry the saddle without fear of nicks and damage. It is water repellent and has a sturdy zipper closure to keep out moisture. The standard measurements are perfect for a variety of sized saddles. It has handles and a shoulder strap that make it easy to carry. It includes a subtle Z-print logo.