Hello my AST sister!!! I graduated from the Alpha Gamma chapter in Arkansas, but I'm now working as a Greek Advisor in Virginia.
I would check out
www.higheredjobs.com. You can search by state. Depending on the university, you may not be able to get a Director position with just a Bachelors, however you might be able to get something in the Student Affairs office (or working with just one council instead of all of them) with a Bachelors. Or get a different job at a school (like Admissions or something) and become heavily involved with the Greek system to get some experience.
Are you looking at getting a Master's degree anytime soon? PM me anytime you want!!
Tau Love,
PsychTau