Unlock the Armory

If your character has some intelligence and a good speech skill then go to the armory on Level 3 of Vault 13 (the locked door with the red light and guard). Tell her that you need more ammunition and then ask who has access. You'll then get the option to say that "it sounds like only the people who need it have access" and then that you "have need". If you can persuade her, then she will open the armory door for you. Inside you will find a Shotgun and lots of ammunition.