Turning any in line, fixed rear wheel, steerable front wheel vehicle is done by countersteering, period. On a bicycle, it is very subtle and you don't realise you are doing it but that is how its done. Racers know this and use it to be able to go around corners fast. Look at a race and you don't see guys throwing thier weight around on a bike to make it lean and turn. Their upper bodies are perfectly still and then they are leaned over hard, all done by countersteering.

As others have said, try this on a motorcycle and you will immediately see that countersteering is how its done. You have to really wrench on the bars to get a moto to lean at 100 mph.

The reason most people tend to fall over when they first ride a bike is because counter steering is not intuitive. You think, if I want to turn right, turn the bars to the right. Wrong, fall over.

There was an experiment done on a motorcycle where a second set of bars was welded to the head tube. The normal bars were just loose, not locked in place. Nobody could get the bike to steer in any usable or predictable fashion using only the bars welded to the headtube.