This is part of the Brotherhood mission “The Lost Patrol”. The only way to open the bunker is by interacting with the terminal outside. However, you won't b able to interact with the terminal if you're not doing the related quest yet.
In the last leg of the "Lost Patrol" quest and after talking to Paladin Brandis inside, he’ll give you permission to take whatever you want inside the bunker. There’s a fusion core from the generator right in front of the door. Aside from that, there’s only a handful of ammo you can loot from the boxes and the steamer trunk near the bed.