It's essentially a BA provided service, though the bus driver is contracted to BA. The gate agent and apron TRM would be BA.

Was this the late 767 service? I really should not justify rudeness (is being shouted at rude if a large crowd has to be addressed?) but there is a lot of pressure to get a big plane loaded fast and off on time. Frankly those passengers who hog the entrance area coincidentally often seem to not understand polite invitations to allow more people on, whereas some assertiveness does tend to work. See Canary Wharf tube station at 5:30pm! The alternative, which I guess means 3 buses and a gentle pace of life, could easily add a 15 minute delay.