I'm not really sure how the American government works in terms of it's structure etc, but if the 9/11 attacks were indeed an inside job, is it possible it could have been done behind Bush's back?

Possible, but unlikely. If the matter was some sort of hidden agenda, then the reactions of the president of the United States would have been crucial to know ahead of time. As many jokes as circulate around Bush (and as little respect as I have for the man as a scientist), there is no denying that one does not, Illuminati be damned, become the president of the country without a great deal of political savvy. There would have been little way to predict his actions without him being part of the project (not that I believe any such project exists).