It has been awhile since I was at Bettis, but I don't remember a school per se. Naval personnel and Bettis Lab people worked there, as well as contractors. There were some technical training there, but the only aspect I knew was the RCT training, which was in accordance with and certified to Navy Shipyard standards.
I think you would need to become an employee of the Lab or join the Navy to attend whatever school it is which you are interested.