Bullets don't move at the speed of light.[1] Shoot a bullet backwards off a bullet train, that bullet's ground speed is less than if shot from the ground while stationary. Similarly, shoot a bullet forward off a bullet train, that bullet's ground speed is more than if shot from the ground from a stationary position. Shoot bullets backwards off a jet moving Mach 3 (just sayin') those 1700mph bullets will still be moving in the forward direction of the jet at 600mph relative to the ground.
But the bullet will still hit the plane following you at roughly 1700mph (you could say, the plane will crash into the bullet at that speed, but it‘s the same result), because it‘s also moving at Mach 3.
But the guy that is pursuing you will still be going after you in around Mach 3 so he will go through your bullets like they would be traveling his direction at 600mph.
[1] They should use rear-facing lasers!