You should assess the sensitivity of situation, keeping note of that how much stress is the bully causing you and how much it is affecting you.
You should not stay quiet at such activities as this gives them more courage and they keep on doing such activities. You might not be a fan of doing argument or having a conflict but note that, if you say silent it will only make things worse.
Keep track of all the bullying activities he does. You should also use the word file and make a chart of it, keeping track of date, time and incident so when required, you will be able to argue with evidence.
Try talking to him/her alone and explain that his/her activities are wrong and he/she should stop harassing you, telling him/her how you are affected by such activities.
If proved useless, you should have a talk with your supervisor. Show him/her the sheet you maintained and explain all the incidents as if he/she ignores your concern, the supervisor can play a pivotal role in teaching sense to him/her.
If any of the above efforts fail, you should file a case to take a legal action against him/her.