Would 9/11 have even happened under Bush? If the former Texas governor cared as little for civil liberties as is sometimes claimed (ironic considering most who claim such firmly supported President Gore's USA PATRIOT Act), then the 19 hijackers might have been stopped either from pursuing light lessons, or from leaving Logan International Airport.
I think it would have... nothing about Bush's stated goals indicated that he was planning on turning the USA into a police state, or even going so far as to tighten up the border or airport security. I just don't think it would have occurred to him. Frankly, the 9/11 planning started in Clinton's day, and no one caught it then, and it continued into Gore's administration, and they didn't catch it either. I can't imagine anything Bush would have done differently.