while land may be vacant it most certainly is NOT 'unowned'. Get a county map. If neccessary go to the County Land office. Get a 'Plat' map book. It shows who owns what property for the entire county. You will find much land is state or 'public' land.
To go shooting on 'unowned' land invites being arrested for armed trespass. Get the map book and be safe.
What do you have against organized ranges?
A firearm in plain view on a motorcycle is just 'open carry' so it should not be a problem. I see bikers with pistols all the time.