From Fast Company, a piece on why the bicycle remains a scientific mystery.

Perhaps it's so laughably simplistic and obviously worthless as a theory that the article didn't even find it worth mentioning, but I wonder if any of the investigators has ever taken the handlebars off of a bike to see how far it rolls before falling over without them as compared to with them?

Isn't a bike subject to the same laws of physics as a tightrope walker?

Maybe, like a tightrope walker, humans have an innate gyroscopic stabilizing sense and that enters into the stability of bike riding.

Yes, but as I read the article they were testing bicycle stability with and without riders.

Pretty much. Our vestibular system has a series of looped canals in our inner ears that provide us with the sense of three dimensional movement, including acceleration.

It is, however, tightly linked with our vision system and can be deceived when our eyes don't have a clear view ahead. The Kobe Bryant accident is believed to be due to this spatial disorientation (which I have also experienced).