After getting rescued by Dutch, interact with the locker to proceed with the character customization screen where you can (permanently) determine your character’s basic looks. Don’t worry about the outfit since you can freely change them from your main menu.
After customizing your character, find Dutch and talk to him. Next, take the Hope County Map, Dutch’s Key, and the handgun from the safe near the doorway. You can also check out various interactable objects, loot containers, and grab some ammo while inside the bunker if you want. When you’re ready to continue, follow the mission marker to the ladder leading to the bunker’s hatch. Mission complete.