Bullet speeds in a space shooter

I encountered some flaws in my gameengine regarding bulletspeeds. In most sample codes you will find that bullets regardless of the shooters speed are moved at a constant rate. But is it not true that you have to add the shooters speed to the bulletspeed at the time a bullet leaves the muzzle ? In fact in both cases as i accelerate the player ship along its z-axis the optical length of the way the bullets travel across the screen vary. This looks odd. I hope i have made my problem clear enough. If anyone has a idea how the speeds should be computed correctly please help.

Thank you