The bully is obviously in the wrong and you’re understandably frustrated. But I think it’s a bit much to escalate to the principal or the parents. I think it’s fine to solicit help from the teacher, but from there, leave it up to the teacher.
The core issue is that your daughter is really sensitive. I don’t say that to excuse the bully or blame your daughter in any way. But if she’s as sensitive as you say, this is going to happen over and over. Not necessarily with the same bully, but in one way or another. And I don’t think you can constantly turn to teachers/principals/others to solve these problems. Or at least, I don’t think that’s the best way to help your daughter, because she needs to learn to better manage these situations. She may still be too young to expect much of her, but in general, I think your focus should be more inward (what you can do to help prepare her for these situations) and less outward.
Edit: What Slim said more efficiently than I did...