The object of "ride" is the vehicle (or animal). Don't say "My mom rides me" to mean "My mom gives me a ride." I ride a horse, I ride a bicycle, I ride a scooter.
Yes, it can mean that. The usual assumption, if you said that someon gives you a ride, would be that the person is driving a car and you are a passenger. If it's something other than a car, we would probably say what (as you did with the scooter).