I haven't played against very experienced ZSS players, but here's what I think:
- Nair should beat out her down B (by hitting her as soon as she's vulnerable)
- Flare Blitz through her Paralyzer, especially if she charges them.
- Try the JC/sliding Rock Smash against her side B.
- You don't want to be directly above her. Ever. Up B can kill, and Up Smash covers a lot of options... except maybe Rock Smash.
- Her grab is mediocre, so shielding should be safer than usual. Don't turtle too much, though.
- If you use Flamethrower, stop as soon as she escapes. She can easily use Down B to attack.
- She's pretty light, so try to get a feel for her kill %s. Fly has some armor on it, so if it trades with her up B, or the first hit of her F-air, chances are she's dead.