My son has raised one against a bullying boss. Son has no protected characteristics, but (from the one sided version I've heard) the boss does seem awful. I've also seen text messages she's sent him, sometimes up to 30 a day on his day off. I don't expect he's been perfect, but her behaviour does seem odd.
Anyway my advice, which he ignored, was that HR work for the company, not the employees, and really the best thing he could do was look for another job if he couldn't work with her.
He was determined she should get her comeuppance and put together a detailed grievance. He followed the policy and did a good his of the letter IMO, although I obviously don't know for sure if it was factual.
They took 11 weeks to respond, well outside of their own process and the investigation seems to have consisted of asking her about the allegations which she's denied. He gave dates, times and witnesses but they haven't followed up on any of that.
He's been moved to another branch, with a much longer commute and whilst they suggested there might be some money to compensate, that hasn't been forthcoming.
He's currently applying for other jobs, but is the lesson that there's never anything to be gained from using the grievance policy?