First of ll let me say that there is way too many people thinking that bullies are really cowards.
Yes, they may be the first to run but it's not out of cowardice, it is more about saving their own skin, as all they care about is themselves.
I have dealt with many different types of bullies across my lifetime, and had to laugh when I was even accused of being one by a teacher, when another student who was our group leader just dumped the entire assignment on the group and I told him off for it. He was the bully and I called him on it, and I got blamed. What a laugh, but not at the time.
All bullies care about are themselves, and they look for ways to put others into service to make their lives better without having to do it for themselves.
Bullies have sociopathic tendencies and are often narcissistic. They do not care who they hurt or what they do as long as their needs are getting met.
So yes, childhood bullies do end up being adult bullies. Once a person has found out how to get their way, do you really think they are just going to stop using a successful tactic? Heck no, not on your life.