Yes, Mormons are allowed to ride motorbikes. The term "Mormon" typically refers to members of The Church of Jesus Christ of Latter-day Saints (LDS Church), and there are no specific restrictions within the LDS teachings against riding motorcycles or participating in related recreational activities.
The LDS Church teaches its members to follow principles of health, safety, and good judgment in all aspects of their lives, including leisure activities.
It's worth noting that some specific guidelines and recommendations related to safety and modesty may exist within local congregations or cultural contexts. Still, these are often left to the individual's personal discretion or may be subject to local cultural customs rather than being universal rules or doctrines of the LDS Church.
If you have specific concerns or questions regarding the teachings or practices of Mormons regarding motorcycles or any other activity, it is best to consult with local leaders of the LDS Church or members who can provide more specific information based on their particular community or congregation.