Forgive me if somebody said this in the 7 pages but there is so much confusion about this.
Countersteering does not make the bike turn! Countersteering makes the bike fall or lean which is required for the bike to turn at speed unless you have a side car
Once the bike is leaning you actually turn the bars in the direction of the turn, which also stops the bike from falling over completely.
At high speed the lean is great but the turn is small. In fact at very high speed even the largest radius turn requires max lean. With exception of racing conditions traction will give up before reaching this limit.
At lower speed and sharp turns you can achieve full steering lock at full lean.
At low speed, slight turn you can use body position instead of lean to balance.
Also, you can slide the rear out so power at the back tire will push you around the corner. Ussually done on low traction surfaces but low traction will also get the front tire sliding too.