When you ride a bicycle, the angular velocity of the wheels is in the same direction as the rotation of the wheels, which is clockwise for the front wheel and counterclockwise for the rear wheel (assuming you are seated on the bicycle and moving forward).
To clarify, when viewed from the side of the bicycle, the front wheel rotates clockwise, and the rear wheel rotates counterclockwise. The angular velocity vector points along the axis of rotation of the wheels, which in this case, is parallel to the axle of each wheel. Therefore, the angular velocity of both wheels points in the same direction as the rotation of the wheels.