The Bardenas Desert is a natural park just north of Tudela and there's one road that crosses the full desert. It may look like the biggest wet dream for off road riders, but as said, it's a natural park, accessible, as long as you stay on the roads (park rangers are nice as long as you keep to the speed limit and stay on the roads). When it's raining or it has rained the previous days stay clear. If you want to know why watch the movie: Lost in La Mancha...