A headwind will slow a bullet down, a tailwind will speed the bullet up a bit.
A tail-wind doesn't speed up a bullet. The bullet is slowing from the millisecond that it is no longer under the influence of pressured gases in the barrel.
The effect of a tailwind or headwind is exactly the same as if the bullet had the same speed difference in stationary air.
In other words, a 3,000fps bullet with a 20fps headwind will slow at exactly the same rate as a 3,020fps bullet in stationary air.
The same bullet with a 20fps tailwind will slow at the same rate as a 2,980fps bullet in stationary air.
The bullet has no idea if it is moving or the air is moving around it.
Of course, the actual effect at any given instant is a bit complex, requiring calculus... as Δt approaches 0 and whatnot...
Still happily answering to the call-sign Peetza.
The problem, as you so eloquently put it, is choice.
He is no fool who gives what he can not keep to gain what he can not lose.
-Jim Eliott, paraphrasing Philip Henry.