Revealing the solution

Okay if we take the distance between A and B to be d
and Bird's speed=V
Wind speed=W

Then the time taken is given by the table below.

V is always bigger than V-W²/V,

thus 2d/v is always smaller than 2d/(V-W²/V)

(if more people share the same pie, the individual pieces get smaller.)

And so we can see that the time taken with wind is always longer.

Next topic (damn interesting): modular arithmetic and how 9+5=2