I actually agree with you on the Martial Arts classes. I have not ever taken Karate, Jujitsu or Judo, but I have taken Tai Chi classes. Don't laugh. Little old ladies make fantastic company, especially when they're feeling younger and younger every day from doing Tai Chi.
Because of the practice, my hand-eye coordination has never been better. I feel confidant and exude confidence when I walk down the street. I am better aware of my surroundings and myself. My reflexes have significantly improved as well.
All of this helps me on the bike. While I'm lucky enough to have only been harassed and never touched or had things thrown at me, I have been cut off and crashed into the car as a result (please see latest post). I am positive that the reflexes I've developed from Tai Chi helped me to stay relaxed during the impact and the fall, and I'm hardly hurt.
So many ways to suffer on a bike, so little time...