On Newsnight last night the whistleblower said Raab is a bully because he stared hard at senior civil servants, and told people to stop as he didn't understand what they were saying, and asked someone else to explain the point - together with other undescribed microaggressions.
It seems to me that Raab is not very pleasant and perhaps fairly ineffective in getting people to work productively.
However, the things said by the whistleblower don't sound like bullying to me. It sounds like civil servants whinging (fairly or unfairly) about being asked or told (fairly or unfairly) for clarifications or more/better/faster work.
Later in the interview the whistleblower said he had changed at the Ministry of Justice, and as evidence, offered the fact that he bought coffees for his staff. To me, this doesn't indicate anything at all and shows that the whistleblower is a bit of an idiot, frankly. Buying coffees for your coworkers is maybe a nice gesture but it wouldn't make Raab less of a bully, if he was one.
Of course, more might come out, and of course the line between unpleasantness and bullying is not well-defined so it would be best to steer well clear of it. However, so far all the allegations by this particular whistleblower seem like fairly common office politics in any high pressure job.