In the summer of 1999, Tuker Carlson wrote a piece for Talk magazine on then-governor Bush that wasn't taken very well by his staff, because Carlson noted that Bush used profanity, something that apparently isn't appreciated by voters. Bush's campaign deputy finance chairman, Jack Oliver, called Carlson after the piece was published and screamed profanities. Carlson observed that the Bush team covered up any and all references to Bush using profanities, and many accused Carlson of lying, that Bush never says the "F-word" even though he does all the time according to Carlson.
Also reported here: Salon.com's "A noble hypocrisy"
Roberto Rivera points to Bush's Talk magazine interview with conservative journalist Tucker Carlson, in which Bush used the F-word and made light of Karla Faye Tucker, a Texas double murderer and religious convert who is much admired among evangelicals.
So it would seem Tuker Carlson says Bush did say the f-word with no evidence to bake up his statement which has been disputed by Bush.
I did find that Bush used the f-word in privately while describing Saddam Hussein and also in private referred to a New York Times reporter as an a--hole. Links below: