If cars had been as popular as guns when the U.S. Bill of Rights was written, then such a right might have been included.
Hypothetically, "Motorized transportation, being necessary to the mobility of a free State, the right of the people to keep and drive automobiles shall not be infringed."
Imagine the vehicles we would have. For one thing, the impossible-to-meet CAFE standards, which make it economically infeasible to sell compact pickup trucks in the U.S., would probably have been declared unconstitutional. On the other hand, laws requiring seatbelts and airbags probably would have also been unconstitutional.