http://socrates.berkeley.edu/%7Efajans/Teaching/bicycles.htm...
with plots of torque-vs-time and analysis here:
http://socrates.berkeley.edu/~fajans/pub/pdffiles/SteerBikeA...
The author spends most of his time at CERN, but got interested in bike physics for a couple of years.
Let's say you want to turn left. We know from experience that you will be leaning left when you turn: meaning, your weight is going to be on the left hand side of your wheels. (The common-sense explanation works really well because I'm not going to explain why you need to lean left to steer left, I'm just going to take it as a given.)
The basic-physics question is: if you're starting totally vertical, how the heck do you get your body mass to be on the left hand side of the wheels in the first place?
You can get a little bit of effect, of course, by simply leaning over left: but that leans the bicycle to the right because you can only lean over one way by pushing your bicycle the other way... and when you do this the bicycle briefly opposes you in the way it's leaning before your gravity can win out. That's less good.
So what your brain has actually learned to reflexively do is, to send your wheels going off to the right while your body continues in a straight line, hence your mass is now over the left-hand side of your bicycle and there is no competition. You then steer into the turn and complete it normally.
I can steer pretty well without hands. It seems as if I must be able to initiate the left lean without pushing the handlebars right.
So why couldn't I also do this when not riding without hands?
Pay attention to yourself next time you ride and you might be surprised.
The momentum from the flick your body creates begins to turn the wheel a small amount, and the forward momentum of the bike in combination with the lean keeps the wheel turned right. By contrast, if you flicked the bike/wheel but did not lean, the wheel would simply straighten itself again.
Even for automobiles this stuff is very simple suspension + steering mechanics. Due to how their suspension & steering components are designed, and assuming they are aligned properly, a car will always follow the road. If the road leans + curves, so does their steering.
Fun fact: when I read about it I had to test and I had to make sure I wasn't deceiving myself so I put one palm in front of the handle on one side and the other one behind the handle on the other side. That way I could ensure I pushed it the correct way.
It worked exactly as advertised (50cc bike so somewhere below 60km/h).
Much simpler than using slow motion camera etc.
Thinking about it though, I think I did countersteer in order to drop into bowls while riding vert BMX.
Edit: I should mention in mountain biking you are frequently dealing with a low traction environment, which I think has a large impact on the techniques.
https://en.wikipedia.org/wiki/Countersteering#Countersteerin...
But yeah, hypothetically lower inertia = more ability to steer with weight, obviously.
This PDF explains it very well, with illustrations, on the last page:
http://bicycle.tudelft.nl/schwab/Bicycle/DO-07-3-2bicycles.p...
"Practically nobody is conscious of the fact that they must steer briefly to the left ion order to make a right-hand turn. But this is not so strange, because the swerve is very small (approximately 3 degrees) and happens very quickly – 0.5 seconds. The wet tire tracks from cycling experiments reveal that we all do this. Apparently we learn this unconsciously when we learn to ride a bike."