I could well get this completely arse up with wind resistances and terminal velocities coming to to play but I think at all sensible speeds the speed of the bullet is still going to be relative to the speed of the gun it is fired from.
Lets say it leaves the barrel at a velocity of 10m/s, since the gun is travelling at the same speed as the plane to get the bullets velocity relative to someone standing stationary on the earth you add the speed bullet to the speed of the plane
So even if you fire the bullet when you are traveling mach 3 the bullet still leaves the barrel traveling 10m/s faster then that
Edit Doh! S. got in while I was typing