1. The Covering for His Own Inadequacies Bully
This is your archetypical bully cliché, but it's grounded in reality. These bullies are horrifically self-conscious, and they're just lashing out at whoever's handy because they're afraid that if they don't, they're going to be the one picked out and picked on. We've all been here; it's called high school (also Congress, but I repeat myself).
These bullies are fairly common in your average Raid Finder run. Just yesterday, I ran a RF with Shelam, my blood death knight. Now, Shelam has an average ilevel of 378 and has tanked all of RF before, but he was called out and almost vote-kicked by three players: another blood DK who was trying to tank while dual-wielding Souldrinkers (a big no-no), his friend and guildmate the last-on-meters fire mage, and an unholy death knight who was fully gemmed for stamina despite being a DPS class. They all called me out for being undergeared, most likely because I was the easiest target in the raid due to my lone remaining blue item, an ilevel 346 helm. Had they not gone after me, it would have been easy for them to have been the recipients of some harsh (if accurate) words, so they chose to go on the attack instead. That let them redirect the blame and their insecurity onto me while feeling empowered because they were making accusations instead of fielding them.
2. The You're a Threat to My Gear Drops Bully
Less Psych 101 and more Seminar: People are Jerks. Remember three things: First, that you're raiding in WoW. Second, you're raiding on the internet, essentially playing a game with the proletariat. Third, WoW raids are loot-based. While people might run the Raid Finder once for the lore aspect, the ones who are running it weekly are there for loot.
In the case of the above example, I was competition for all three of those players' Vanquisher token drops and competition for the other death knight's tanking gear. Trying to orchestrate a vote kick in order to lessen the competition for loot drops is a powerful motivator for players, and their main way of doing it is convincing the rest of the raid that you're not worth keeping. It's petty and rude and self-centered ... and you should probably expect it.
3. The Elitist Egotist Bully
This is mostly likely the worst kind of bully you'll find in the Raid Finder, mainly because there's not much you can do about them. The group of bullies I've belonged to in the past, these are your heroic mode raiders who deign to grace your RF group with their presence so that they can take their Dragonwrath, Tarecgosa's Rest, top meters and then call you all bad for not doing the same. These are the ones who are going to complain every time you get loot, not because they need it but because you don't deserve it.
Please note that I'm not saying this about all heroic raiders. This doesn't even apply to most heroic raiders. There will, however, always be people who believe in their own superiority, and damn you for not being one of them. This is the type of bully I'm most familiar with, mainly because this was me for a time. This still is me at times, but I'm now mature enough to keep my opinions to myself when I'm having a bad day.