[peterwwillis]

Yep. If you try to just lean right immediately, the bike will just.... fall over, because the wheel stayed straight.

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.