The most slimming exercise is actually jumping rope, assuming you are not trying to build big muscles, but just achieve slimness.
When you are young, all you see are flaws in yourself, even when there are none. If you could take the focus off yourself and take an interest in other things, you would become a more interesting person and more attractive to people, ironically.
I doubt this is the answer you are looking for, but here goes.
You realize you are seeing your flaws through a distorted lens, right? Are you in therapy? No matter how thin your thighs and bum are or are not, you will likely see them as flaws through your bulimic eyes until you tackle bulimia. The very best exercises to give best results in these areas would be exercises to target your perceptions. Good luck.