In normal conditions, when a biker banks, the normal force can use friction from the road to balance the horizontal component of the biker's weight. This leads to a turn because to balance the horizontal and offset-vertical weight, friction from the road creates a force acting inward along a curve; a centripetal force. This counters a torque around the center of mass of the system and allows the biker to both not fall and turn.
On a frictionless road, there would be no horizontal component of force to balance the weight of the biker whenever they shift off of a perfectly balanced system. The center of mass of the bike-biker system would experience the full force of gravity minus the normal force. However, when offset (either in a banking turn or just a minor offset from perfect balance) the normal force becomes less than the force of gravity because of trigonometry. The ground contact point (the wheels) now exert a torque around the center of mass. The horizontal component of weight (again due to trigonometry) is no longer balanced at the contact point. This means a few things: First, the net force on the biker is now not zero; there is a net force down and so they will fall. Second, there is a net horizontal force on the wheels due to the weight of the bike and biker, which means the wheels will slip. And thrid, there is a net torque around the center of mass due to the normal force, which means the system will rotate such that the biker will move groundwards.
What this illustrates is not only could one not turn through banking, but biking in general on a frictionless road would be just as hard as sitting on a stationary bike without it falling over. One would be in an unstable state, any shift of weight away from a perfectly balanced state would cause the biker to fall.