Firstly I usually fall into the trap. I take people on face value unless proved otherwise. So I start out answering the posts...it takes me a while to 'get there'...like the man at Bethesda " While I was coming another stepped into the water first." 
It takes a while for me to 'clue-in'. @Job usually 'get's it much quicker than I do.
Once I 'pick-up' on another spirit , I then try to expose, then back off.
Why waste time. We've had some of late on the site.
(But with those that we are familiar with, I don't discern the same 'false-spirit'. ) I feel they enjoy it as young boys like rough-housing and wrestling. It sounds hostile sometimes, but I don't feel that it really is.
The reason I involve ...is in thinking ( probably foolishly) that maybe, just maybe, I will say something that God can use to speak to them in some kind of balance. But really that is all 'hot air', and it just falls to the ground and rolls off the into the corner of the screen, not making a blip! :)
One always hopes for redemption in both fellowship and relationship.
But I haven't seen that really work on a dogmatic bully that has his/her mind already made up.
Bottom line..I see a great difference between a bully who is "top- dogging- it", and wants to have the very last word...than a divisive spirit that tries to pull down, destroy peace, and challenge faith. That is a totally different kind of bully!! That is the slippery kind..
Like Job said..silence/ignore works best of all....with no audience, that spirit gets hungry, so has to find a different home for it's bully-food.
Job usually gets there first...but I am close on his heels in 'getting-there' and sniffing out the thing. :)
Ok so I really enjoyed your response and I want to address several points.
1. You mentioned that it takes you a while to catch on to the spirit of the bully - this is interesting and I think it illustrates a difference between polemics or agenda-focused communication and simply dialogue. I have engaged in both types on this board. In the past, I tried to be a 'reasonable pundit' for Catholicism. My assumption was that all people wanted more knowledge and if I could give them clear and accurate knowledge about the RCC they would be thankful and either respectfully agree with me or respectfully disagree. My assumption was based on my experience (of course), I once had inaccurate views about Catholicism and then, I learned new information that pursauded me to investigate the church and pray about it. Where I went wrong in my thinking was to assume that other people are as ignorant about Catholicism as I once was. Also, I assumed that people are persuaded by information. Neither ideas are true. My respect for people's knowledge base, pathway to changing their mind, and reason for belief has improved over the years.
2. You mentioned the difference between the bully you know and the stranger. I have adopted this distinction at times, but recently, I have questioned it. I recognize today, a 'rough and tumble' person with my point of view, is often someone's else's bully. Trump is a hero to many Americans. I have been forced to look at the bullying behaviors of the person rather than their tribal affiliation, when making a personal assessment. Just because someone is Catholic for example, doesn't mean I should blind myself to abhorrent behavior.
3. You mentioned getting hooked by the bully into believing 'if they just knew' they would stop bullying. Yep. I get it and I definitely get hooked. Unless I am able to step back, and recognize that the person is valuing ideas, polemics, being right, over neighbor, and that I am called to do the opposite; I get hooked into a battle of wills, using information as ammunition in order to be 'right'.
4. You talked about different kinds of bullies. I am not sure I agree. I think all bullies pretend to be pushing a shared agenda and fain loyalty to a cause or doctrine, but when everything gets boiled away, they are really about dictating control; whether it is how the 'shared' doctrine is interpreted or who gets membership into the 'club' they are promoting - they usually assert their right to be the 'decider'.
Thanks for your post!