A cynical person would say the better the bully can perceive possible negative consequences coming towards himself, the less likely he is to bully - and that's the only difference between children and adults.
Hence the mob mentality. There's strength in numbers, which makes it important to belong to the group no matter what. The bullying emphasizes the difference between being "on the bus" and "off the bus".
Adults are a little more sophisticated in their thought process and realize the negative consequences don't have to happen at that instant to be negative. The fact that the victim knows what happened and has avenues to bring bad consequences on the bully stifles the bullying.
Absent those constraints, say a town where it's acceptable to bully a minority group, not only do you have the same pre-adolescent levels of bullying such as saying this is your water fountain and this is mine, etc, but adults can step it up to another level, to the point of lynchings, killings, etc.
Or, if an adult is in a situation where he feels total control, such as with a child, the bullying can jump to sexual molestation, etc.
An adult's ability to see and avoid bad consequences in the future is main reason for adults not bullying as much as kids do. The change in behavior (avoiding bad consequences) comes first, and then the kids or adults slowly bring their morals into line with their behavior.
A more optimistic person would say changing the morals via education comes first, and then is followed by a change in behavior.
I think there's probably a mix between both, since there's many kids that are a little more capable of empathy and see the reactions of the other person as a negative consequence and never really develop a habit of bullying (but it would be a very rare child that didn't at least give it a go to see what happens). And maybe even a few of the childhood bullies develop empathy, it just took them longer to develop it. But there are a lot of people who are only kept in line by the fear of negative consequences and it's only the improved ability to perceive possible negative consequences that change their behavior.