Yes, the kinetic energy of the ball thrown inside a moving bus depends on the speed of the moving bus. This is because the speed of the bus adds up to the speed with which the ball is thrown inside the moving bus.

For instance, If the bus is moving at a speed of 24 km/hr and a person inside the bus throws a ball with a speed of 26 km/hr in the same direction as that of the motion of the bus. Then, for a person inside the bus, the K.E= 1/2 x m x (24)². But, for a person who is static and is outside the bus, the K.E of the ball=1/2 x m x (24+26)². Hence, the motion of the bus affects the K.E of the ball.