I'm not sure how long it will take them, but if they do suspect anything they won't tell your parents or anything, they just want to help. You can tell them as much or as little as you choose.
Here's a link on how to help protect your teeth from stomach acid:
http://www.umanitoba.ca/outreach/wisdomtooth/bulimia.htm
I was 19 when the dentist figured and she snitched....