There may be conflicting perceptions of what is going on. You see it as a concert where there happens to be a bar in the room. The bar staff may believe their job is to serve drinks and the music is something which takes place in the background. If it is a general audience (which appears to be the case if they are not familiar with folk club etiquette) then they may take a similar view.

You need to agree with the pub manager how the event can be managed to meet both parties' requirements. I think you should deal with the manager rather than individual staff.

If it is held in a public bar then I don't think you can expect folk club rules to apply. However if it is in a private function room which includes a bar that is a different matter, and you can ask the manager to ask the bar staff to keep the noise down during performances.