Personally, I found ignoring the few bullies I encountered in school to be pretty effective, but I'm also aware that what I experienced was pretty tame compared to some stories I've heard.
Our bullying stopped when we fought back, or moved out of school. And yes the bullying continues to hunt us to this day.
One way of doing that, that many people have found successful, is to not let them bother you. If you're no longer interesting to bully, they'll ignore you for someone who is.
So, in some cases you may only need to push back to the point where you're not the easiest target in the room. ie, you don't always have to be the fastest runner to get away from animal who is looking for easy prey. You just have to be faster than the slowest runner.
I have to agree with the sentiment expressed elsewhere in the thread, that bullies bully for different reasons. The only time I have been bullied, avoidance and not showing a response worked, because the bully had low self-esteem and was looking for acceptance from his peers by picking on smaller kids. When he saw that he wasn't getting anywhere with that, he stopped.
I can tell from experience that this is not how it works. Real bullies never leave you alone until you stand up and fight back. It's the amount of energy it takes for them to bully, not the amount of damage they do.
They don't care how resilient you are or whether you care about the bullying or not, when their bullying doesn't have any bad consequences or the potential for bad consequences. Only if you make it hard for bullies to bully it stops.