Daily Bunker Buster missions in Destiny 2 are a new addition in Season of the Worthy. You can get access to one each day, as the active Bunkers in the game. At the moment, the only active Bunker is at the Sludge on the EDZ, but more will be popping up on the Moon, and Io, as the season progresses.
You can find them by heading into the Bunker itself and heading for the large door behind Rasputin’s main node that hangs from the ceiling. Legendary Lost Sectors will not be active until you finish the Bunker Buster mission each day. Interact with the door to open it, then head inside to find lots of enemies crawling around inside the main Bunker. You will need to go from room to room, taking out all the enemies before you move on.
Some of the enemies will be Champions, the most common ones that we have run into so far are Barrier and Overload, so you will need your mods from the seasonal Artifact to be able to finish the Bunker. Remember, those mods will only nullify the effects of one kind of enemy, so make sure you have a couple of weapons that can take the different mods types, and have it all set up before you go inside.
When you get through the last room of enemies, you will need to interact with a button to extend some stairs to leave, then just head back to Rasputin. There isn’t much to it, but you do get some Warmind Bits for completing it, and a piece of Legendary Gear.
Mostly it seems to just exist to give you something to clear to get back to a Legendary Lost Sector, but it might tie into something more important later in the season.