I've played a good Oli a couple times and from my limited understanding of the matchup, Oli can't camp ZSS the way he can to many, many other characters (running away with pikmin toss and pivot grab being his camping strategy).
My random thoughts:
Side-B outranges his grab ever so slightly (even with blues I think) and I think the only way pikmin toss interrupts side-B is if he throws purples, but keeping purples in stock weakens his grab game. The paralyzer disrupts him nicely too.
He does rack damage very well if you don't keep him in check and he can kill ZSS fairly early if you get caught. ZSS can pressure him well, but you have to be very wary of the dmg you are absorbing from the pikmin that will get tossed at you. Clearing them off becomes top priority, but you have to do it in a way that does not leave you open but at the same time, does not let the pressure off him too much, as the less time you give him to pull pikmin, the better.
It's also hard to ledgecamp him with dsmash because he can drop down, then jump and up-air through the stage, then re-tether. Side-B can still be used to ledgecamp him though and he can only re-tether 3 times before he must touch the stage again.
I think overall she gimps him better than he gimps her.
I don't she she's necessarily worse off on the ground than the air, as he has aerials that you need to be careful of and your range on the ground is superior.
All in all, it seems like a pretty even fight to me, though I might tip it just a little towards ZSS b/c I think she can control the pace better than he can. However, I don't think it's anything that can't be managed by an Oli who knows the matchup well.
If you are looking for an Oli COUNTER, then ZSS is probably not your character.