Jinx's Mini-gun should be automatic, not burst.
It's a MINI-GUN. It should be full auto.
Attack Speed could affect by determining the speed at which it spins and therefor actually fires bullets, but it should be constantly going not fired in little bursts.
I understand she was made burst fire to use the same attack coding as the champions who don't have fully automatic guns, but I can't imagine it would be hard to make her different. Blizzard already did it with Tracer in HoTS.
If it was needed for balance you could also give her an ammo and reload system; but in any case it probably wouldn't be needed because the individual bullets would have really low damage, to balance out the sheer number of them.
She's be like the opposite of Jhin as far as basic attacks go.
[slayer-jinx-wink]