The best way to stop someone who is not following the rules of civil discourse (and might be a bully) is to confront them on the spot and allow the community to see it so they can also respond.

Private messaging only exposes you to more without any protection. And if you hit a spot, it can become much worse because of defensive attacking that happens in private so there is no way to feel safe about it.

In groups, there are things called "process time" where when something disrupts the balance, you take time out to process what is going on and then return to the discussion at hand. This is a tried and true method for dealing with problems in a mature and responsible way that is fair to everyone and restores civility and safety.