Bait her, and ledgecamp to get rid of the item pieces. Intelligent Capes are the other way to deal with those item pieces.
Don't Cape Stall against the D-smash. While Ness, G&W, and Lucas can absorb it, your Cape does not reflect it. It's the only hitbox in the game with that precise set of properties.
Ducking is super good against ZSS. I don't have a list of things you can duck under yet, but she literally can't hit you with any aerial but a perfectly spaced N-air if you duck (shield the D-air on reaction if she ever does it). Other things I want to see if you can duck under...Dash Attack and U-tilt. I strongly suspect this is the case. Ducking at certain ranges I think also can avoid her SideB, though I wouldn't count on it.
When in doubt, shield against ZSS. She has very few ways around it.
All in all you want to get past her SideB range and then play from there. She'll try to throw you off with some Dash Attacks here and there, and she'll try to U-air or U-tilt out of shield if she thinks she's in trouble (both of which I think you can duck under, correct me otherwise). Generally if you don't let her hit you with her D-smash, SideB, or any random aerials, she shouldn't be able to kill you easily.
FLUDD seems to be good for edgeguarding her, but I'm still not entirely sure how to edgeguard ZSS's Down-B kick.