It is important to report the incidents of bullying that take place at the workplace. However, you must understand that HR will not be able to take action unless there is evidence against the bully. It is important to keep a record of who, what, when, where and why things are happening at your workplace. This will help you give concrete examples of the behaviour of the bully and you will be able to recount the exact details if and when asked to.
There will be a point where the bullying is intolerable and is taking a toll on the mental health of the victim. He/she will want to tell their supervisor or HR about it and find a solution to the ongoing problem. They will definitely ask for some sort of evidence that will help strengthen your case. You can start filing away emails, record phone calls, and messages or even maintain a diary to keep track of the date and time of the incidents. It is important that you have enough evidence to prove the bully is trying to belittle you and make you feel bad about your work and yourself.