What rights do I have if I am being bullied by my manager?

Speak to the personnel department. They should have workplace manuals on how bullying is dealt with. If they don't have policies, then speak to your lawyer because it is a form of harassment and may well be actionable through law. Harassment, bullying, intimidation and the like are completely unacceptable in any workplace and a manager has no excuses given his or her role of responsibility and level of experience. And don't trust anyone who insist that you have somehow created this situation -- that is absolute circular drivel from which you can never escape. The bully must take complete responsibility for their own bad behavior.