I can only quote from the military side having seen this as a manager. That said, I suspect civil procedures are quite similar.
Firstly, make sure that you are as objective as possible in you evidence gathering. Ultimately you will get into some form of "He said, she said" type argument.
If you don't feel you can challenge the individual head-on, go to your unit Equal Opportunities Advisor. They are well trained, selected for their attributes and, importantly, are completely trustworthy.
Decide what outcome you want. It is pointless making a complaint if you don't want a particular resolution. I had one young lady who just wanted me to know she was being harassed; she didn't want me to do anything about it. In my mind, that is not good enough.
Respect the bully's anonymity. If you want to remain anonymous, so should they.
Don't dwell on things.
Make sure someone (the EO advisor?) thoroughly explains the procedure - you need to understand it. Proone is not definitive.
Good luck.