I've used a duffel bag many times, too. REI has some fairly strong but lightweight ones.

But I've been touring on my Bike Friday folder for many years and it packs into a hard-sided suitcase. I've usually been able to store it at the place where I spend at least my first night and last night. Another option would be to query some folks who live near your arrival point on the warmshowers.org list and see if someone can store it for you in their home while you're touring.