Hi OP.
So....a working man's club...?
How long have you worked there?
Your Unite rep will likely raise this on your behalf as a grievance or will ask that you do this yourself.
You need to spend some time thinking about your specific concerns (I.E when you say you're being bullied...you should come up with specific incidents, dates and times and any witnesses.....also an explanation if you're raising issues that aren't recent and you didn't report them at the time (perhaps you were in fear to report them)).
If you cant come up with specific incidents, this will be difficult for you to progress.
If it is a working man's club (or something similar)....it would not be unusual for voluntary members of the committee to hold your grievance meeting and conduct any investigations.....just giving you the heads up about that. If they're impartial, then this would be deemed acceptable. It doesn't have to be a paid member if staff.
If you do not feel the person who is assigned to your case is impartial then you and your union need to make a huge song and dance over that (this may force them to engage with a completely impartial, external consultant).
Keep your eye on things after you've raised your grievance......it isn't unusual for committee members (and the accused....especially if he's in drink) to discuss your case openly with each other and other customers........gossip.....at the bar......if this was to happen it would obviously be something else to add to your grievance.
It would be highly unusual for committee members (and, in my experience, Chairs/Bar Managers/Stewards) to be competent in employment issues....also giving you the heads up about that.
Unite are sh*t hot at what they do.
Might you also add to your grievance that the bully is in breach of health and safety regulations by attending work in drink?
Suggest to them that they need to conduct an urgent assessment in to the risk of this individual attending work in drink (if there is a risk...this can be sufficient grounds for him to be removed frkm the workplace). Also tell them that the Club will be vicariously liable if they are aware this person is attending work in drink and something then happens to him, you or your colleagues or customers as a result of this....there is no doubt about this).
Also....if you can tag any of this bullying behaviour to one or more of the protected characteristics......they will (or should) shite themselves about that. Protected characteristics include sex, pregnancy/maternity, race, religion, disability, age, sexuality (have a Google of them).
If you do tag your complaint onto a protected characteristic (not saying you should do if there isn't an obvious problem)....then you will be protected from any unfair treatment as a result of raising that complaint.
This will include ensuring you do not continue to be subject to a hostile working environment after your complaint has been raised.....some workplaces suspend the accused to ensure this. It also means not cutting your hours....nor moving your working area or anything else that disadvantages you.
If you do raise that complaint formally, you should expect a formal invite to a grievance meeting with the right to be accompanied and sufficient notice. You should also be given the option to appeal if you're unhappy with the decision.
Let us know what Unite rep has to say....I am confident they'll be able to assist you.....the ones I have met (many, many) are extremely knowledgable and competent.