An alternate definition of "bully" as a noun means someone who harasses or intimidates. The modern definition of "bully pulpit" reflects the misuse of the church pulpit by unenlightened preachers to bully followers into submitting to their twisted views.
This term was coined by President Theodore Roosevelt, who referred to the American presidency as a "bully pulpit," by which he meant a terrific platform from which persuasively to advocate an agenda. Roosevelt often used the word bully as an adjective meaning "superb" or "wonderful" (a more common expression in his time than it is today). A pulpit is the elevated platform used by a preacher. The term has no relationship to the word bully in the sense of a "harasser".