Talk to the guard to be able to become an Initiate
Visit a satellite base of the Brotherhood of Steel in NCR, Den, or San Francisco to apply for membership with the door guard. Membership is considered through high skills or by bringing 200 AP 5mm round or 20 AP rockets.
Fulfilling any of these requirements gives the player the rank of Recruit, the lowest rank in the Brotherhood of Steel. Access is then granted to all three bunkers in towns.