How to properly take care of Zoe

There's a few things that can be done, in my opinion. Pick one of the following, and she should be fine.

1.) Shorten the length of her CC. I shouldn't be vulnerable to taking double damage from an already high-burst mage for 2 full seconds. Her bubble hitting you is basically a death sentence, and its not even a hard skillshot to land. The AoE on it is fairly large. That, coupled with the fact that she can 100-0 you long before you can buy a QSS or Zhonyas makes laning against her very oppressive. By the time you can counterplay her, she's already 10/0.

2.) Take away one of the instances of damage on her bubble. This might help her NOT be able to 100-0 you at level 3, which few other (if any?) champions can do.

3.) Make her able to be CC'd out of her portal. I can't tell you how many times I, or a team mate, have landed a stun or root on her when she pops up, only to have her disappear anyway. The blink happens fast enough that it takes some skill to reliably land some CC on her while she appears. Players that are fast enough to capitalize on that should be able to, and the CC should stick then and there - not follow her back to her original position. LeBlanc can be stunned when she blinks, why can't Zoe? Zed can be stunned when he throws his shadow... The only other champions in the game that CC interacts with this way are Tristana and Ezreal - neither of which have NEARLY the same burst potential as Zoe.

4.) Raise the cooldown on her portal. Being able to just stand over the wall from someone's turret and blink-poke them to oblivion is ridiculous, and hardly fun to play against. Make her have to really think about when to use it, rather than just being able to do it basically whenever.

5.) The whole drowsy/sleep thing. Who else in this game has a 2-part CC like that? Nobody I can think of. Its either a slow or a stun... why is it both? Who thought this was a good idea? Stun me or slow me... doing both with one move is horrible. Especially one that's relatively easy to land.

6.) Again, the whole drowsy/sleep thing. Its either a heavy CC, or its a 2x damage amp. Why is it both? Who thought this was a good idea? What other champion in the game has a heavy CC (Stun, Root, Fear, Surpress) that also amplifies their already ridiculous damage against you by 100%? Nobody I can think of. ESPECIALLY one that is so easy to land, and on such a short cooldown.

7.) Remove the AoE from her Q. If she's gonna be that bursty, fine. If none of these other options work for you, fine. If she's gonna be able to 100-0 people at level 3, fine. At least make it to where she's a single target damage dealer. Make her an assassin. There's no reason she should be able to 100-0 one person if she lands her CC, and then bring everyone around that person to 30-50% hp along with it.

Somethings gotta give. This champion is just unfun to play against. Leaves no room for error, no room for counterplay. Make any mistake at all, and you're dead. Stand next to the person that made the mistake? You're probably still dead.