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Jumping in here since I'm a physicist... JohnKSa pretty much has it right.
Warrior Poet: You really can't ignore air resistance and expect to get a solution that is anywhere near correct. Air resistance is very significant in ballistics. Also, the bullet will remain spin-stabilized until something stops the spin; reaching the apex of a ballistic trajectory does not cause the spin to cease.
One thing about spin-stabilized objects is that you can get interesting behavior, such as precession (like the wobbling of a spinning top). Precession should increase drag somewhat, but some degree of axial stability remains; you won't get actual tumbling until the rotation of the bullet is mostly gone.
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