Are they actually well thought of or are they accepted because of their bullying behaviour and people are too scared to call them out? If everyone says the bully is great, people are scared to stick their head above the parapet and say otherwise.
Keep documenting. Whether you decide to act or not it's handy to have. ACAS are helpful if you don't want to join a union.
You need to know what it is that is happening. Is it bullying? Is it harassment? Is it discrimination? Is it someone doing their job? Try and look at it objectively. I knkw it can be hard when you're the subject but trying to see it from another POV can make it look different.
Is it something you could sort informally? Would a quiet word with the person or their manager or HR sort it? My last manager kept teasing me in front of people. It might have been bullying but I spoke to him and told him I don't like it as it humiliated me, he genuingely didn't realise, was horrified, apologised, bought me a bottle of wine and stopped.
If you decide to act, be realistic about what will happen and what you want to happen. Look at your allegations and evidence, the organisation culture and unfortunately how that person and you are viewed. Basically, who does the organisation prefer? It shouldn't come down to that but often it does. Some organisations are great and will investigate impartially and properly, others won't.
If you act, understand who will and won't be on your side. It takes a strong person to stand up and not everyone is strong. You might lose people you thought were friends, or at least who you thought would have your back. But you can't take it personally, they are probably scared of repocussions.
Bringing an allegation of bullying is hard work. It is scary and emotional. You have to relive everything and you do question yourself. People can distance themselves from you or stab you in the back.
In my case I knew I wouldn't win. It absolutely was bullying and I had evidence no doubt about it but the organisation was weak and my face didn't fit. I knew from the start I would lose my job as a result of my grievance but it got to the point where I had to do something.
The organisation ralied around my bully and senior managers made it clear from the outset I would lose my job. In hindsight I think they were trying to scare me into dropping the allegation.
I think I shocked them because they thought I was weak, over emotional and disorganised. I wasn't and made things very uncomfortable for them for a while.
As I say, it wasn't upheld but that wasn't a shock. I did lose my job as a direct result of my grievance but it made it very difficult for them. I can't go into details but I left very happy.
I know HR reps on here will say, no you didn't lose your job as a result of your grievance and if you did they acted illegally etc but it absolutely was as a direct result of that.
I left, I made things hard for them for a while but I know nothing will change long term. My replacement also experienced bullying and left which says it all really.
In reality they probably laugh about me now if they even think of me.
I kind of think though, I'm proud of myself for making a lot of noise. Sure, nothing changed but I stood up for myself. I ended up out of work but I held my head up as I left and it was more on my terms, than theirs. I made it clear they couldn't do what they did to me and expect me to lie down and take it. It took a while to stand up to them but I did.
It took me a long time to mentally recover from the bullying and the grievance process. Even now, if I get called into an unexpected meeting at work my first thought is panic.
My grievance was hard and I'm not sure I'd recommend people go down that route but it was right for me and I'm glad I did it even if it didn't seem to achieve much for anyone looking in.