The time it takes for a boomerang bird to turn around appears to be based directly on its **momentum**.  If you shoot straight up and trigger it at the apex of its flight, it should change direction immediately because it has no momentum.  On the opposite end of the spectrum is when you trigger it after it's been falling downward for a second -- its direction will barely be altered before it hits the ground since its momentum is high.

The boomerang bird is accelerated directly left if shot to the right, and directly right if shot to the left.  Its up/down momentum and acceleration are not altered.  So if it has no up/down momentum, it will fly directly left/right after the trigger *plus* the effect of gravity (so it will start out directly left and accelerate downward).  If it has some momentum up, for example, it will begin to go leftward/rightward on an upward angle, and accelerate downward due to gravity.