It all depends on how many bios there currently are that need approval, and how much time the moderator that approves has on his hands.
Right now, the amount of bios that need to be looked over are 81, or so it seems. Judging my that, the time it takes for the bio to get approved could be up to a month, although it could also get approved earlier. If I remember correctly, when I posted my bio there were 6 pages of unapproved bios already present, and that ended up taking a month or so, so if I had to guess, I'd say that it would probably be around 2-3 weeks for yours to be approved/declined.
All in all, there really is no definite answer, since it simply depends on the time the moderator has to spend on NB, and on the amount of bios that haven't been checked yet. Just be patient, and before you know it, you will most likely have an answer some time in the near future.