I would protect it with cardboard. As stated previously, you can make your own cardboard mailer. Search google with a search term like this for some ideas: youtube make dvd mailer out of cardboard
You can also protect your dvd(s) easily with cardboard, then place them in a bubble mailer. This video shows one way. You could cut the flaps from boxes to give you a piece of cardboard to protect the dvd's with. The following video will give you an idea of how that's done:
https://www.youtube.com/watch?v=hYVIPjUpib0
I have boxes for mailing dvd's and videos that I've purchased (before I began making boxes), but now I often just make my own. It's good to know how to make boxes since having a properly sized box can save a lot of postage costs, and it helps not to have to purchase boxes.
Another helpful youtube video is
https://www.youtube.com/watch?v=d-QGl1EKrlI
