I just started playing New Vegas and am trying to get into the NCR correctional facility without a fight. I grabbed a Powder Ganger outfit and bribed the guard to get in, but when I approach the door, he starts shooting me. Does anyone know what I'm doing wrong?

You are doing nothing wrong. The mechanic is set up so you are disguised and no one is the wiser---except guards. Guards are NPCs that can sniff you out from a mile away and are marked on your compass by the telltale red pip on your compass. Just sneak attack this guard, pick up his key, and walk on in.