What does 骑在 someone's 头上 mean?
The figurative meaning  of 骑在~头上 (ride on top of someone) is not 'to bully ~' , It is 'to dominate/ to rule over' For example: "Mr.A graduated one year before you(have been your senior schoolmate for all your college life); entered the same company one year before you and has always been your boss." -- You can say Mr.A  一直骑在你的头上 (always ride on top of you) meaning he's always been your boss or having authority over you.

If one day, you got promoted to higher position than Mr.A, then you are in fact 反过来骑在他头上 ( turn around and ride on top of him)

One more example: "他一直被妻子骑在头上" (he has been ridden on top by his wife) meaning his wife is the head on the household over him. 

As long as she always at the top of the family, no matter how well she treats him, the fact that she's riding on top of him remains.