You may think bulimia isn't causing you any problems or that you can deal with it, but believe me, it will cause you problems. The problems associated with bulimia are so many, I don't even know where to begin. Fact is, it is already affecting your health, even if you don't know it. (i am assuming that you throw up your food?) I threw up for two years before I began to have serious problems. I have now permanently damaged my stomach valve, and my teeth were rotting quite a bit. And that was only after two years! If you haven't seen any effects yet, you will sooner or later. Sorry to be so blunt, but there's no way you can assume that bulimia will not cause you any problems.
In the course of your illness, you adjust to all the difficulties you experience as a result of your bingeing-purging behaviour (at least in my experience). That means, you keep devising new ways to hide your illness from others. Thus, you think you can manage and you've got it under control. But you don't realise that bulimia is actually controlling you, it's ruling your life. Maybe you should take a few moments and think about all the changes in your life as a result of bulimia. Can you eat out with friends without problems? Can you go to the restaurant, or a dinner party without panicking? Can you treat yourself to something delicious without feeling guilty and like a loser, and vomiting afterwards? Can you enjoy life without constantly worrying at the back of your mind about how you look and how much you weigh?
For me, the answer to these questions was no, no, no. I have been in therapy for over a year and it's doing me a world of good. Sure, I did get strong urges to cancel the appointment every single time, and sometimes I still do get the urge. But I always resist those urges, because it won't do me any good, and the therapist gets his money anyway, so the only one who loses out is yourself.
I haven't vomited in two months, and I feel infinitely better for it. Therapy has played a major role in my recovery process. The fact that you get upset and desperate after cancelling an appointment, as you stated in your post, shows that you have a problem and are not happy. I would strongly advise you to keep those appointments! You are not doing yourself any good at all. And you may think you can stop purging any time, but the longer you leave it, the harder it gets, because it is an addictive behaviour, i'm sure you're aware of that. Even alcoholics, smokers etc. Think they can stop any time, but the truth is, you are hooked, and you need a lot of help and support, as well as willpower, to stop. Please don't wait until you experience a major health scare! Life is far too short.
If you don't want help, I do understand, I was like that for a while. I even enjoyed being bulimic, in a way, because it "allowed" me to eat as much as I wanted and still lose weight (i thought). The truth is, you do gain back more and more weight over the years, and you feel so terrible, life becomes agony. Everything revolves around food and vomiting it up again, and you lose out so much on the nice things in life (friendship etc.). I bitterly regret the years I wasted, and the fact that my body is now damaged, and for what? You will one day wake up and want help. I know you will. Please let that be sooner rather than later. I wish you all the best. I hope you will find the strength to realise that you need to change your life, like I did. Good luck.