A busby is a tall fur hat worn as part of a dress uniform by some British soldiers, especially horse soldiers. It looks grand on parade and in old photos. You will almost never meet it as an everyday hat; it belongs to army and ceremony talk, and to tourists looking at London. People often mix it up with a bearskin, the even taller black fur hat worn by the Foot Guards you see outside palaces. A busby is usually a bit shorter, and it often has a cloth bag hanging down one side. Though actually, even British speakers get the two hats confused, so if you mix them up you are in good company — but a careful book will keep them apart. It has nothing to do with a bus, and nothing to do with being busy.