Twisted Treeline Co-op vs AI is the fastest way to earn EXP, since you only need to defeat the bots in a minimum time of 7 minutes to earn EXP rewards. Usually you can defeat the bots even faster than that, but it will be so fast the game won't reward you. Even faster if you have a duo or trio coordinating with each other.
Considering Jinx's passive, and how easy it is to generally get kills on bots, that's a lot of free attack speed (because of the buff she got this patch), which makes her ideal for just an outright shoving strategy even at super early levels. So all you need to do is just go pure damage. It's even more obvious considering they are taking alacrity for even more attack speed (and the precision tree in general gives bonus attack speed). And then demolish for the extra damage against turrets. With that much free attack speed, press the attack can proc very easily, which causes Jinx to get excited when you get easy kills, making everything else proc super easy and... well, you understand.
I think the general strategy is just to bum-rush bot lane all the way to their Nexus.
If you were to get a double XP boost (a timed one obviously if you're playing that many games a day), then I think you make around 80~90 XP per game.