I think you misunderstand the constitution.
It outlines how the federal government is organized, delineates certain powers granted to the Federal government, then very obviously switches gears in the Bill of Rights and starts to outline everything the federal government does NOT have the power to do.
And just in case they missed anything out, the 9th and 10th amendments to the bill of rights are abundantly clear:
Amendment IX
"The enumeration in the Constitution, of certain rights, shall not be construed to deny or disparage others retained by the people."
Translation: any other rights held by the people and not enumerated within, shall not be denied just because they're not listed here.
And
Amendment IX
"The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people."
Translation: The federal government can ONLY do what is specifically listed here.
So just because possession of a car is not listed in the constitution, does not mean that the right to travel is not a basic right. Furthermore I see nowhere in the constitution anything that gives the Federal government any power to oversee travel within the USA; given the 10th amendment then, they do not have this power.