So how long does it take to fix a bug?

Depends on the issue, how long it takes them to find it, or even realize it exists for that matter, I'm still seeing the jhin ult morde bug, where if mord ults jhin and kills him while hes ulting on his 4th shot, the jhin ghost will perma do the 4th shot damage and crit until its killed... Several people have stated this and it's still very real and happening. Who knows how long itll take for them to even notice this one :/

You can expect whatever bug aatrox has to be resolved in a day or so more than likely since it's already at their attention.