Hello there. First of all, I'm not an rp mod and therefore not someone who checks bios, but I have a bit of an idea how it works. Considering there are more than one mod checking them, this might not apply for all. Also, rp mods, correct me if I'm wrong, but here is the deal according to me.
As far as my knowledge on this topic goes, bios are getting checked in order of submission, thus indeed first come first serve. However, there are cases where this does not apply. As Caliburn is not around at the moment, some bios might get checked with a (slight) delay. These are the bios of moderators, senseis, certain special ability bios and bios where the new rp moderators are not sure of. When you (considering the first two on that list are not for you) have a special ability in your bio which the mod that is currently checking the bios is told not to check, or if there are vague things in your bio, or anything else that might make them doubt whether to approve or decline your bio, they will leave them be until Caliburn returns, as Caliburn is rp administrator and the one that is able to check the above named biographies.
If you have the feeling that none of the above named cases is the case of your bio, then just be patient. Patience is a virtue.
It will be checked sooner or later in any case.
Hope this solved your problem/question.
Cheers.