Most companies, well lets face it employees and employers don't like hassle and don't know how to handle these things.
Unless you have very knowledgable and competant people in charge they will bodge it up and you will end up leaving.
My sister was bullied at a local council by a woman who was known to be a bully. My sister had witnesses, sworn statements and kept a diary about what was going on but they still found in favour of the bully. It's often not what is right but who the bully knows.
It is probably cheeper and easier to get rid of you then the bully as they have probably been there a lot longer then you and is of a higher grade.