I want to date my ex-girlfriend's best friend/roommate, what do I do?

Not a good idea! Think about it this way - you would be directly interfering in your ex-girlfriend's relationship with her roommate. If anything is to come of your wish to date the roommate the least destructive direction would be if the roommate made the move toward you first. Even then it's problematic. I doubt your ex is going to offer up her roommate for you to date. That would be more a fantasy than reality.