it is not true with uniform speed. but it is true if it moves with uniform velocity.
we can prove it by: suppose the plane moves at 3i+4j i.e. 3 units along x-axis and 4 along y-axis. at this instant bomb is dropped. it gets same velocity and follows a projectile. its horizontal velocity does not change as there is no acceleration along horizontal direction. the plane is also not changing its horizontal velocity. so they remain below one another and due to different vertical velocities, they dont co-incide.