How common is bullying in academia?Fairly common, though the form and extent depends on the field. This answer is about a "micro" example: not a person being pursued but a particular kind of single incident.
In economics (and I believe in other fields as well), the following dynamic sometimes happens in a seminar where someone is presenting his or her  research.
Someone knowledgeable asks a question about a detail of the analysis. The speaker's answer reveals that he didn't know something important or didn't think through the issue. In any case, the answer reveals weakness. So somebody follows up, and the second question---along with the answer, perhaps---reveals even more clearly there is a hole, growing in apparent size, that the speaker was not prepared to address. (Sometimes the speaker will have a few sentences intended to address the issue, but the audience clearly feels the response is superficial or otherwise inadequate. Or they simply don't understand what's being said.)
This is the crucial moment: Once people "smell blood", in certain cultures, they attack. They will call attention to other issues, which might have been too minor to bring up or easily addressed had things gone differently. But now every criticism feels like it subtracts from the speaker's credibility, and so there's this bad feedback loop. Often at some point it gets somewhat awkward, so people ease up and let the speaker finish the talk, but by now he's usually depressed and people are visibly disengaged.
I have only seen this happen a few times, but when it happens, it's pretty unpleasant for everyone and has a bullying flavor, though usually no individual in the audience actually wants to hurt the speaker. Speakers who are too timid or too assertive are more susceptible to this phenomenon. To generalize, these are people who don't fit naturally into the culture of their field---so, more often minorities.
 I'll use male pronouns for brevity.