When a bicycle is in motion & speeding up the force of friction exerted by the ground on the two wheels is such that it acts 

When the bicycle is speeding up , a torque is applied on the axle of rear wheel . Since the rear wheel is not slipping on the ground, force of friction must act on the rear wheel in the forward direction which accelerates the bicycle .When the bicycle is moving in the forward direction ,a force is applied on the axie of the front wheel in the foward direction by the frame .Since the front wheel is not slipping , force of friction on the front wheel must act in the backward direction . This frictional force produces a torque about the axle of the front wheel due to which angular velocity of the front wheel gradually increases .