Here is my reasoning:

So, yes, we all know the English language is supposed to be one of the most grammatically difficult languages around.  But when you think about the rules, almost all of them have some basis in logic.  The reason that the English language provides two indefinite articles (both "a" and "an") is based in phonetics.  It is difficult to pronounce "a" in front of any word beginning in a vowel.  For example, saying "a apple" or "a egg" requires a lot more gutteral maneuvering than saying "an article."  Pronouncing a vowel next to a consonant makes it so we don't have to keep flexing the back of our throat and instead are able to speak with our tongues, teeth, and lips (the parts that make the consonant sounds!).  

 To use "a" in front of an acronym like "FBI" would defeat the purpose for which the rule was created because when you say "FBI," you begin by pronouncing "ehhh" not "ffff." 

 Conclusion: "an FBI agent" takes the cake.

"This is an BSA rule." could be interpreted as "This is NBSA rule."