This is not an adult Bar-Mitzvah; rather it is an Orthodox tradition that a chosson, groom, gets an aliyah a week before his wedding. Usually he does not read from the Torah, but many Sefardim do. Usually only the members of the congregation attend and sometimes the groom's close friends come as well.
This is generally called an "aufruf" -- yiddish for call-up -- because they call him up to the Torah. It is done in middle of the Shabbat prayers between Shacharit (the morning service) and Mussaf (the additional service), usually at the end of the Torah reading, unless the groom is a Kohen or Levi. The time on the invitation is usually the time of the beginning of prayers but it is possible that they gave an estimate of the "call-up".
No need to attend if you are attending the wedding, but it is definitely a very nice gesture, and the groom will surely appreciate it. It is customary to throw candy on the groom at the conclusion of his "call-up". Some also sing and everyone wishes the groom "Mazel Tov".