A

When a bomb is released from a horizontally flying airplane, it is influenced by gravity, which acts downward. Initially, the bomb has the same horizontal velocity as the airplane, and the only force acting on it after release is gravity. As time passes, the bomb will fall downward while continuing to move horizontally. This creates a path that is characteristic of projectile motion, which is a parabolic trajectory.
Therefore, the correct answer is A: a parabola.