A bully pulpit is a position sufficiently conspicuous to provide an opportunity to speak out and be listened to.
This term was coined by President Theodore Roosevelt, who referred to the White House as a "bully pulpit", by which he meant a terrific platform from which to advocate an agenda. Roosevelt famously used the word bully as an adjective meaning "superb" or "wonderful", a more common usage in his time than it is today. (Another expression which survives from this era is "bully for you", synonymous with "good for you".)
Its meaning in this sense is only distantly related to the modern form of "bully", which means "harasser of the weak". The word is related to the Dutch boel, meaning lover, and buhler, meaning a rival for a lady's affection. In English usage around 1700, "bully" came to be similar to "pimp", which gives us the connotation of a ruffian or harasser.