Do you have the right to marry or buy a toaster? Do you have a right to whistle while you walk down a sidewalk? Do you even have a right to walk down the sidewalk? Or the right to walk at all? None of these things are spelled out in the Constitution.
Newsflash: American citizens have more rights than just those explicitly spelled out in the Constitution. The Constitution didn't have to grant people the right to own horses, and yet many did, and were free to ride them without government licensing, registration, or fees, and this is even on government postal roads. Where in the Constitution is the power for any government agency to regulate private transportation spelled out?
You have it backwards.
Following your logic, the blind and infants have the right to drive a Hummer on the interstate or on the sidewalk for that matter.
Your question: "Where in the Constitution is the power for any government agency to regulate private transportation spelled out? "
The answer: Article 1, Section 8, clause 3.