Can you be covered by your parent's motorcycle insurance?
Good question! I know when I was in college and high school my parents owned our cars but I always had one at school that I drove.
To make certain you can, call or e-mail your prospective insurers and ask the question. Also, if they say that you would be covered, get it in writing and make sure that you are one of the covered drivers on the policy. Usually a policy will either specify who is covered by name in the policy, or they will cover all persons living in the household so if someone borrows the vehicle they are covered under the owner's policy.
Good luck with your search and compare quotes. It may help save you some money. Don't rely on what you think is covered, get it first hand from the insurance company and get it in writing to protect yourself.