The point is not to let him fill his blood well to the brim. Scare the shit out of him whenever you can. And if you can't do that, take him late-game where he can't do too much aside from initiate (his range isn't THAT fantastic under his ultimate).
I got a chance to toy with Aatrox on my friend's PBE, and this is the "knowledge" I have to share about fighting him
I would say that Aatrox's hardest counter is Teemo. I say this due to the blind and constant harass, Teemo can Move Quick to dodge the knockup from Dark Flight as well as Aatrox's skillshot, and Teemo can stand on a mushroom, bait a Dark Flight and Aatrox is probably dead or forced to burn his passive.
Aatrox is overall pretty weak to lane bullies (ex. Rumble, Darius) because they deny his farm, and if he can't farm properly, Aatrox will fall off rather quickly.
That said, don't expect laning against Aatrox early to be a bloodbath even though he's fairly aggressive and pushy.
Dark Flight's health cost is rather high - if he misses it, you can pounce on him.
All of his abilities barring his ultimate scale off AD. A Ninja Tabi in lane is not a bad idea.