"Colonel Windsor to Bomber Command - send in a bomber and stop those pesky Imperials from reaching their Airbase! " - Colonel Windsor. Bomber Command is a sub-branch of the Anglo Airforce, (presumably there is a Fighter Command, though it is never mentioned).
As the name implies, Bomber Command is in command of all of the Anglo Isles' Merseychester Bombers and bombing operations. The command appears to have considerable power and influence as, despite being the apparent head of the airforce, Pierce states, "Bomber Command have ordered that we defend this airbase". This raises the possibility that Pierce may only lead Fighter Command, not the entire airforce.
Bomber Command have a large role in both the Solar and Anglo Campaigns. In "Anglo Attack", Windsor ordered Bomber Command to send in bombers on multiple occasions in an effort to take the nearby airbase.
Later, in the Anglo Campaign, Bomber Command provided bombers for Windsor's mission to clean up Windsor's Column (if the players loses both bombers, Windsor comments that Bomber Command "won't be too happy").
Finally, Bomber Command ordered Pierce and the player to defend the Anglo Airbase in "Their Finest Hour", before ordering the capture of A-Qira's airbase so that the Anglo Airforce could destroy the Solar Fleet.
Judging from the high number of Merseychester Bombers the player destroys in Battalion Wars 2, it can be assumed that Bomber Command's forces are severely depleted by the end of the game.