A non-Jew doesn't need to have a Bar Mitzvah... If his mother is not Jewish he should consider following the Noachide laws. Either that or he should go through a conversion to Judaism... It makes no sense to give a non-Jew a Bar Mitzvah if he has no idea what a mitzvah is....
I would recommend that he seek out an Orthodox Rabbi who can explain to him how this works... I certainly encourage him, if he is truly interested in being Jewish, to convert.