Like Sen Loyd Bentson's son, who was also in the 147th. Both he and Bush are on the same Federal Recognition orders as 2nd Lt's.
Those federal recognition orders (I looked at mine from the OK ANG last night) are what made Bush (and Benson) part of the US Air Force. It made them part of the ANGUS, which is a reserve component of the Air Force. Their other "hat" is as a TxANG, but it's hat rarely worn, especially for pilots. -