Spell out, never abbreviate. Follow the practice of the U.S. Air Force, which uses Air Force base as part of the proper name for its bases in the United States and air base for its installations abroad. Some bases have become joint bases with other services.
On second reference: the Air Force base, the air base, or the base.
√ Lackland Air Force Base
For American facilities located overseas, use air base:
√ Bagram Air Base