Private travel in Xinjiang on motorcycle

Special tours to China such as self-driving, hiking, cycling, horse-riding, hot air balloon, or other expeditions should provide an original copy of "Invitation Letter of Duly Authorized Unit" or "Confirmation Letter of Invitation" issued by China National Tourism Administration or the tourism administration of related province, autonomous region or municipality directly under the Central Government.
You can travel on your own in Xinjiang, which is allowed. But as you are not familiar with the route, you'd better hire a local guide. I'm not so clear about the customs regulations. But I think you don't need to pay to take the motorcycle in since you'll later take it out.