A bicyclist has to tilt the bike X degrees off the vertical towards the center of the circle to create sufficient centripetal force to remain on the circle. This is usually discussed within the context of a bicyclist negotiating a curve on a path.
Value of X (how much to tilt or lean) is calculable from equation inside the circle (m is mass of bike and rider, g is acceleration due to gravity, v is the velocity of the bike, and R is radius of the circle).
If X is too large (i.e. rider tilts too much into the circle), centripetal force will be too much and the bike will start turning into a circle with radius smaller than R. If X is not large enough, there won't be sufficient force to keep the bike on the circle and the bike will veer off, turning in a circle with radius larger than R.
Balance equation in the circle tells us that to reduce X, the rider needs to create an opposite force larger than the existing value of the right hand side of the equation. This can be done by increasing v (velocity) in the numerator, reducing R (radius) in the denominator, or doing both.
