Exiting a bully culture carries additional risks for targets

A bully culture can be challenging, especially if you're on the receiving end.  We should be clear that workplace bullies are trying to force their targets to resign or be fired by torturing them. Their tactics are often successful but leaving can complicate matters further for vulnerable workers.  

One of the difficulties targets face is obtaining a solid reference that is not tainted by workplace bullying. References from one's current employer can be essential for obtaining a new position. If you have been the victim of workplace bullying, your boss may be able to sabotage your job search by giving you the wrong type of reference.
I recommend that you get a letter of recommendation from an ally or someone outside your department who can serve as a solid reference prior to leaving. It does not have to be from your boss.

You should also think about whether you want your potential employer to contact your former employers. It is more difficult to mark yes when a worker is part of a bully culture. If a target marks yes, there is a greater risk that their boss will keep bullying them. 
However, if a target marks no, there may be asked about an explanation. There are a lot of risks involved in marking yes or no. As a result, careful consideration is required.
Targets can also be exposed to additional risk if they jump from frying pan to fire. Consequently, if you do not screen for workplace bullying, you may end up in another bully culture. To avoid another difficult workplace, check out this article on How to Screen for Bully Culture. 
Bully culture can cause additional harm to vulnerable workers and targets if they don't plan ahead.