Personally I don't like to lose my pieces for any reason. I figure I have the advantage- the pieces start at my feet, not theirs, I have a (sexy) glide toss, they might not, I have a lot of mobility which helps me fetch pieces quickly, and most of all I simply have more practice using pieces since I'm ZSS while they aren't as likely to have the same.
If I'm charged, a downtoss from standing makes it bounce of the floor and is a tricky way to upset things quickly before they get the match in their favor. Mostly, however, I love throwing once piece, having them shield it, and right after that follow up with a glide tossed second piece into any move, picking them right back up where they bounced off and toss them both again. The majority of the time that gets them off their feet, and with more than one piece nearby you can hit with one and then follow up with another very quickly. For example, throwing one at them after they get in the air, they airdodge catch it, I throw another at them out of the airdodge and they never get a chance to toss it back at me.
Also, on the stages with things to bounce the pieces off of, the suit parts can become absolutely brutal. For example, Green Hill Zone, where not only the pieces bounce off the hills at great angles making even a missed throw disruptive and damaging, it also piles them all nicely for you on the bottom. Finally, since that course has walk-offs, it's easy to get some percent and smack them with a piece and KO them before the pieces ever disappear.
Since you can catch thrown items by dash attacking, ZSS is good at catching or picking parts back up with her good dash attack, and often when they go for the parts when they are still on top of a passable platform, it's creates the perfect opening to jump up and uair them from underneath, which also gets another piece for you.