Not an explicitly enumerated right in the USA, but a "right" in the same way freedom to walk down the sidewalk is a "right": you're not endangering peoples' lives & it's not explicitly prohibited so you "have a right" to do it. If someone attempted to prevent you from walking down the sidewalk they would be denying you that "right."
Driving a motor vehicle does endanger peoples' lives, so we (society) decided you don't have the "right" to do it, but you can be granted the privilege to do so pretty easily provided you have the $$ for administrative fees & can pass a test demonstrating basic competency.
Your question is totally reasonable, but I think it's fair to say one has a "right" to bike on public roads (barring interstates) but not a "right" to drive on public roads as this requires a license & is subject to many strict regulations.
What exception makes "barring interstates" okay but not "barring roads with a speed limit >X"? Not saying I necessarily disagree, just trying to understand your reasoning.
One possibility: Interstates are big roads that make it faster to get somewhere you could get on another road if you didn't mind going slower. Some (esp. rural) roads with 45+mph speed limits are the only way to get somewhere, therefor bikes need access. Anyway I'm also just waxing; I don't know the exact laws and surely there are exceptions- generally speaking "all but Interstate" seems like a reasonable thumbrule.
There are places not accessible by roads with bike-accessible speed limits. Those are much more common than places not accessible except by interstate. (Incidentally, biking on the shoulder of the interstate is permissible in my state, with the occasional exception of some cities and bridges without shoulders.)
I am interested in why sequoia asserts that it's correct (or at least permissible) to prohibit bicycles from interstates but a violation of rights to prohibit them from other roads. The fact that bicycles are not prohibited from all interstates seems somewhat orthogonal...
I think it's reasonable to designate certain very-high-speed roads as "car only" when there are reasonable alternative routes for bikes. If there's a destination you can only get to by interstate I'd say "allow bikes." I'm a biker and strongly pro bike-rights but I recognize that certain exceptions are reasonable for safety & expediency. :)
So hypothetically, you wouldn't object (on "rights" grounds) if there were a non-interstate that was labeled no-bikes when there were plenty of alternate routes to everywhere serviced by that thoroughfare. Sounds reasonable to me.
Minor nitpick: bicycling also endangers lives. And even though it doesn't happen often, reckless cycling habits may endanger motorists' lives too (by e.g. causing swerving through unpredictable behaviour). I say that as someone who commutes to work by bike.
This is regrettably untrue. There are far fewer deaths from bicyclists, of course, but if you google you'll see that there's about one a year. Although I'm pro-cycling I have to say I particularly dislike that segment of cycling community which seems to have the attitude that they not only have right of way at all times against cars, but also against pedestrians; I have had far more near-misses from careless or rule-breaking cyclists than with cars.
One per year? Compared to cars, food poisoning, bathtubs, ladders, and almost anything else you can think of, that's close enough to zero to be a non-issue.
The actual language differs from state to state, but in general there is no attempt by the states to revoke certain individuals' right of riding a bicycle. (For example, being pulled over for drunk bicycling can get your driver's license suspended, but does not affect bicycling.)
Corollary: When states declare that bicycles on public roads are subject to the same rules and responsibilities as cars (and most/all states do), sanctions on bicycling are not available as penalties.
NC General Statute 20-4.01 (49) defines a bicycle as a vehicle with the same rights and responsibilities as other vehicles:
"bicycles shall be deemed vehicles and every rider of a bicycle upon a highway shall be subject to the provisions of this Chapter applicable to the driver of a vehicle"
That's a bold claim. Citation?