Does one "drive" a motorcycle or "ride" it?

Solution 1:

If you are driving the motorcycle you are riding it. If you are on the back while someone else is driving it, you are riding on it.

Solution 2:

The terminology is left over from the days before motorized conveyances, where to "drive" horses or cattle was to induce them to move in a desired direction. People "rode" horses by sitting on them. People "drove" carriages by inducing the horses pulling them to move. People "rode in" carriages or "rode on" wagons when they weren't the driver.

So now,

• if something is a one-person mechanical conveyance you sit on, like a horse, you "ride" it.
• if something looks more like a carriage than a horse, you "drive" it.
• If something looks more like a carriage than a horse, and you are not controlling it, you "ride in" or "ride on" it (depending on whether you are inside or outside).

If elephants (which more than one person can ride) had been more common in England, we might "ride" rather than "drive" cars.