Q. If a Seudas Bar Mitzva is done on Motzei Shabbos a week after the bochur’s birthday (he was born bein hashmoshos, so it could not be done on the prior Shabbos) is it still considered a Seudas Mitzva?

A. Mogen Avrohom (O. H. 225), rules that it is a mitzvah for a father to make a seuda on the day his son becomes Bar Mitzva, as on the day he enters the Chupah.
Mishna Berura (ibid. 8) explains, that the reason for the seuda is; that now his son has become an Ish Yisroel who is obliged in keeping the mitzvos of the Torah. Shaar Hatzion (ibid. 9) quoting Eliahu Rabba, points out as the source for this Halacha, the known Yam Shel Shlomo in Bava Kama (37).
The Maharshal there mentions that there is no greater seudas mitzvah, than the one we make for a Bar Mitzva, since we celebrate and praise Hashem for the opportunity of the former kattan, to now comply with the mitzvohs  as a Metzuveh Veo-se, or one that is required to do them. And we know that godol hametzuve ve-ose mimi she-ayno metzuve ve-ose. Responsa Maharam Brisk (2: 68) mentions that the prime time for this seuda is on the day he becomes Bar Mitzva. The reason some wait until Shabbos is that that is when people are more likely to attend. Piskey Teshuvo (Y.D. 217: 16) quoting Chavos Yoir avers that up to three days after the bo vayom it is still considered a seudas mitzva since the affects and impact are still present. This being similar to the Takonas Ezra of reading the Torah on Monday and Thursday so three days will not elapse without Torah or the three days given after Shabbos for reciting Havdala. Divrei Malkiel (1: 3) asserts that once tefilin have already been donned, there is no more point on making a seudas mitzva unless a drosho is said. Nitey Gavriel (Bar Mitzva 16 n. 2) mentions that it is already customary to wait until Shabbos.
Horav Shlomo Miller’s Shlit’a opinion is that even on the second Shabbos if the Bar Mitzva bochur says a drosho it is considered still a seudas mitzva.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a