What to do with depressed friend, who possibly has body dysmorphic disorder?

BDD is a very difficult problem so I sympathize for your friend. However when a friend's problem starts to affect your well being sometimes the best thing to do is distance yourself. Maybe what your friend needs is losing her best friend to realize that she has to start trying harder to get better. If you are as important to her as she is to you she will make it work, if not then she wasn't that good of a friend. You shouldn't make other people's problems your own, in fact it is behavior that people often take part in to avoid their own problems. Give her an ultimatum that she either resumes therapy (Cognitive Behavioral Therapy would be best for BDD) or you can't be her friend anymore because it is bringing you down.