A classy bitch is like a bitch but being classy about it. Like many people hate bitches, but if you're classy about it people will generally take it in a funny way and not get mad at you for it. It is a great skill to have and it will make your life seem a lot easier.
The best example of a classy bitch i can think of is Jordan on the show Scrubs. If you watch some of the episodes that she is in you will understand what i mean.
It's all about the classiness, and once you've mastered it, you will be able to control people and they will end up acting like your bitch.