For every authoritative-sounding, in-depth explanation, there is an equally plausible, yet conflicting and contradictory alternative.
One is gyroscopic forces. Ever picked up a spinning hard drive? Notice that it feels strangely hard to turn in some directions? Same idea.
The other is the feedback loop consisting of the bicycle and its rider.
If the bike is stationary, it's hard to keep it upright because you have no assistance from gyroscopic forces. At low speeds, you have some assistance but not enough. At higher speeds, the bike wants to maintain its current orientation, and it's easy to feed in the slight corrective forces needed to keep it that way. Hop off the bike and it will keep going until something causes it to veer off course.
You can throw a ton of math at it, as in the paper mentioned elsewhere in the thread, but at the end of the day, gyroscopic forces and negative feedback are all that's necessary. The Schwab paper appears to show that the gyroscopic forces aren't necessary, but no bicycle in the real world is ever going to work that way except in rare corner cases, e.g., if you're one of those riders who can stay upright at a standstill.