Mike Tyson was bullied as well. So were countless other great fighters. In my eyes, that's all the reason you need. Over time, though, you need to find new reasons to keep going. At first, learning to overcome bullying and to defend oneself is all the motivation needed to start. I've found that the main thing that KEEPS one training is a love for the martial arts.
Everybody's reasons are different, though, and that's only my experience.
Good luck.