States differ on their laws regarding if a person with a suspended driver's license can obtain a motorcycle license.
Some states will allow you to have a motorcycle license while others will not allow it while your main driving privileges are suspended. States, such as Maine, have the motorcycle license as an addendum to your regular automobile license so it would be unlikely that you would be able to get it without a valid driver's license.
Also it could depend on the state terms of your suspension, such as if your driver's license is suspended or if your driving privileges are suspended. If it is the latter than it likely means any type of license is suspended for the time period set forth by the court or DMV.
You will need to check with your state's Department of Motor Vehicles to get a definite answer for the question if you can get a motorcycle license while your driver's license is under suspension.
If you do obtain a motorcycle license you can obtain insurance for your bike through this link or by calling our partner Safeco at 1-800-936-0356.