I find that one way to handle bullies in positions of authority is a form of passive aggressiveness where you do your work, but don't engage with them much (maybe a sarcastic smirk once in a while just for your own satisfaction). Standing up to them works in the moment, but doesn't solve the problem because they'll want revenge. Subservience is never a good response because they'll just bully you more quietly. Passive aggressiveness works especially well with extoverts because extroverts (and it's been my observation that most bullies are extroverts)can not handle passive aggressiveness.
Yes, my solution is immature and don't do it anymore, but it works!