You can purchase a motorcycle even without a motorcycle license however you won't be able to ride the motorcycle home without a motorcycle license.
But you certainly can purchase the motorcycle without a motorcycle license and then have someone with a motorcycle license ride the motorcycle to your place or you can put the motorcycle on a motorcycle trailer and trailer the motorcycle home.
But you do not need a motorcycle license to simply purchase a motorcycle.
You will however need the motorcycle license to register and tag and insure the motorcycle though but just to buy the motorcycle doesn't require a motorcycle license.
The same goes for cars and trucks or other vehicles you can purchase vehicles without a drivers license however you just cannot drive the vehicle home without the drivers license.