I think it depends on the sorority... some are very open to alumna initation, and others offer it only for special circumstances or for women who help the local chapters that are not actually members themselves, or for notable community leaders who "uphold all the values of XYZ", and I think there are some that just don't offer it at all.
I've never been involved in alumna initation, but from what I gather, basically it can happen one of two ways:
1) a chapter or alum association may notice someone who is working very hard for XYZ and they would like to extend the invitation for consideration for alumna initation... they volunteer to sponser the said woman and the process begins. she attends events with the alumna association, etc. etc.
2) an interested woman might contact local alumna associations about her interest in alumna initation, and there is a lot of waiting time involved.. once she gets the "ok" she obtains a sponser and goes to events with the alumna association she wants to join and may/may not recieve a "bid" to join
I think aerierising (I KNOW i didn't spell that right!!!) has on her website which NPCs do/do not normally offer AI.
I guess in a sense AI is kind of like informal rush, except with the AA and not a collegiate chapter.