Simoneaux,
I am attending the FAA academy right now (going to Southern California TRACON.) I would STRONGLY recommend not riding your bike to the academy center, as a matter of fact I think it may be a very near impossible feat, due to the extreme inconvenience and very possible danger.
The Aeronautical center is located right next to the Will Rogers Airport (which like most airports is out a ways away from anything and everything, housing etc.) I live relatively near to the center and it is an easy 15 minute drive for me.
Additionally your schedule, like everyone else here, will vary between day and evening shifts 7:00am - 3:30pm and 3:30pm - 12:00am, it will be one or the other. Aside from taking nearly 45 mins to ride your bike (at least), there is no bike lane along the roads to the center which include an unlighted and lengthy backroad if you are coming from the south, and a busy 4 lane highway that comes right off of the freeway if you are coming from the north (like most people.) These would be in my opinion quite dangerous, not to mention the inconvenience of having to huff it on your bike at a very early or late hour in your "business casual" wear.
If you cannot drive it would greatly behoove you to find an apt complex to live in which offers an academy shuttle service to and from the center daily at no cost, (of which there are many) best part, if they are late you are not at fault. Or you can carpool at least as there are many students like yourself especially at complexes that are closer to the academy. Good luck, and let me know if there is anything I can help you with.