I guess it depends on how often you throw up & whether you brush right after. I was bulimic for years & never had a problem with wearing down teeth.
But bulimia does cause osteoporosis, which is when your bones & teeth don't get enough calcium. So your teeth & jawbone get hollow & your teeth fall out before you are very old. I knew a 47-year-old bulimic who had false teeth because of that.
So please try to get help so you can stop this very harmful behavior! There are so many reasons to quit!!!