For cars to turn, the wheels must be turned into the bend so that the frictional force between the road and the tyre has a component perpendicular to the current direction of travel of the car. This component of friction provides the required centripetal force for circular motion.
This centripetal force, unfortunately, has a “side effect”. It produces a torque about the center of mass of the car which tilts the car away from the bend. Why does the car not flip over? Well, if the car turns too sharply, it does flip over. But most of the time, as the car leans outward, the contact force on the inner wheel (which tends to flip the car) drops, and the contact force on the outer wheel (which opposes the flip) increases. This restores rotational equilibrium to the car so it does not slant any further.
This “self-correction” mechanism is however not available to motorbikes since they have only one set of wheels. Instead, motorbike riders must learn to lean into the bend. The shifting of the centre of mass allows them to achieve rotational equilibrium.