Lambzig after years in the job one understands there three sides to every case: the alleged "bully's" side, the employee's side and the truth.
There are some cut and dried cases, for example, a bully takes a witnessed swing at a member of staff but they are very rare. More often there are two sides, there is often a performance issue, there is often an issue where a member of staff thinks they are above management or requires quite robust management to comply and do the job. There are also some managers who are just horrible and everyone agrees but there isn't enough to make a case stick.
No offence meant to you by that paragraph OP; but I am answering Lambzig - am sure you have had a horrid time.
Unfortunately a member of staff can't go to HR and make complaints and expect a magic wand to be waved. Just because a says x about b that does not prove a case. If allegations are made, the employee needs to raise a grievance because that is what will result in a proper investigation. Even if a formal and thorough investigation takes place it is in most cases inconclusive with comments being made about fault on both sides. The most successful tends to be a collective grievance and those are extremely rare because it is a natural instinct for people to keep their head under the parapet at work.
HR cannot take action on the basis of somebody's word. Someone can come and say something like "he said I was a useless, black bitch just like all the rest". That is anecdotal by the way and I do not under any circumstances support such a statement or mean it to be inflammatory. If that isn't witnessed it't word against word and would never stand up at tribunal - the person being accused would have as much of a case as the accusor.
One can investigate until the cows come home, interview a dozen people, and still there is often no robust evidence. The best that usually happens are recommendations for team building, mediation, professional boundaries training and in the meantime relationships are fractured and enormous amounts of tension prevail for very many staff. I have invited two parties to a meeting before to try to get to the bottom of things and sort things out and asserted what the accusor has said for the accusor to sit in the meeting and say "I never said that"; I have also received written complaints saying terrible things that if they were investigated and triangulated would have resulted in dismissal and have said to the instigator this is dreadful and we must investigate only to be told no; they don't want to be the one to bring it into the open and when I have said the concerns are serious and must be investigated I have been accused of bullying them to raise a grievance yet I am castigated for not taking action. The complaints are then withdrawn.
Unfortunately, although there are exceptions, in my experience the majority of grievances stem from underlying performance issues and if you push aside the veil of the grievance there will be serious capability issues underlying it; sometimes on both sides.
The other issue to be aware of is that there are is a tiny percentage of people, especially at present, who actively engage with litigious behaviour and seem to make it a personal mission to try and bring a case in relation to one or other protected characteristic. That doesn't excuse any discrimination whatsoever but there are some very manipulative folk out there.
I'd love to throw up a few real life examples but they would breach confidentiality and out me.
Interested to note the support of the GP's out there; I often feel they fall hook line and sinker for a "story" but I guess they are in the same position as me on may occasions.