Might I ask what sort of job/workplace you are in, and the "Bully's" position relative to you? Boss? Subordinate? or equal footing.
As the others have said, you really don't have a choice but to involve the employer (legally speaking). That being said, I've been in very similar situations, and I'm not known for my tactfulness, and after a few choice words, sometimes bullies realize that you will not be spoken down to etc, and come around, so to speak. I personally would rather approach the person and have it out with them initially, and if that doesn't work, escalate to direct supervisor, and upwards if necessary. Be sure to have a witness to any and all interactions you have with bosses, and the problem individual. Record anything, be that with a notepad or phone etc. A diary becomes legal evidence in such situations I'm lead to believe. I'm not sure on the legality of audio/video recording without someones consent or knowledge.
If you are a member of a union, speak to your delo or rep.
The above it my opinion only, and does not constitute legal advice. I am not a lawyer.