The Gemara (AZ 18b) just mentions “Maaseh Bruria” but does not get into detail. Rashi there goes into detail.
The Ben Yehoyada explains that the student was a S’ris, emasculated, and had no desires. He did look normal though, for the most part (or in most parts). She did not know he was not “manly”. He mentions the bath thing as being “platonic” (my word not his). When she was “busted” she was under such embarrassment that she committed suicide (she was not considered an avaryan because of the severe emotional trauma). When Rabbi Meir realized what he had caused, he went to Galut for a kapara.
See the link to see it inside, bottom left of the page.
http://www.hebrewbooks.org/pdfpager.aspx?req=14476&st=&pgnum=148