Regrettably apocryphal.

When Bonaparte visited Giza during his Nile expedition of 1798 (the story goes), he determined to spend a night alone inside the King’s Chamber, the granite-lined vault that lies precisely in the centre of the pyramid. This chamber is generally acknowledged as the spot where Khufu, the most powerful ruler of Egypt’s Old Kingdom (c.2690-2180 BC), was interred for all eternity, and it still contains the remains of Pharaoh’s sarcophagus—a fractured mass of red stone that is said to ring like a bell when struck.

Having ventured alone into the pyramid’s forbidding interior and navigated its cramped passages armed with nothing but a guttering candle, it's said that Napoleon emerged the next morning white and shaken, and thenceforth refused to answer any questions about what had befallen him that night. Not until 23 years later, as he lay on his death bed, did the emperor at last consent to talk about his experience. Hauling himself painfully upright, he began to speak—only to halt almost immediately with the words you quoted: “Oh, what’s the use. You’d never believe me.”

As I say, the story is not true. Napoleon’s private secretary, De Bourrienne, who was with him in Egypt, reported that he never went inside the tomb. (A separate – and older – tradition suggests that the emperor, as he waited for other members of his party to scale the outside of the pyramid, passed the time calculating that the structure contained sufficient stone to erect a wall around all France 12 feet high and one foot thick.) We also know quite a lot about what happened while the emperor was on his death-bed (a period which extended to 40 days, and so gave him quite a lot of time for recollection); accounts recorded by his valets, Louis-Joseph Marchand and Louis Étienne Saint-Denis, by Grand Marshal Henri Bertrand and General Charles de Montholon, and by his doctor, Francesco Antommachi, all exist. None say anything about his experiences at the Great Pyramid. They also disagree about his final words, which might have been "France… my son… The army…" (Marchand), or "Who retreats" (possibly) and "At the head of the Army" (definitely - Bertrand), or "Head ... army" (Antommachi) or "France ... army... head of the army... Josephine" (Montholon).

That the tale is told at all, however, is testament to the fascination exerted by this most mysterious of monuments–and a reminder that the pyramid’s interior is at least as compelling as its exterior.

The earliest known version of the story that Napoleon had explored the interior of the pyramid is pretty old, though - it originates (minus the quasi-supernatural elements) in W.H. Ireland’s The Napoleon Anecdotes, published in 1822.

Yes, that would be the same William Henry Ireland who 27 years earlier had infamously faked and seen produced at the Theatre Royal, Drury Lane, Vortigern, which purported to be an "undiscovered" play by Shakespeare.

Using Google Books, I attempted to trace the anecdote you cite, complete with quote, back to its Ur version. The earliest account I could find was one written by John Sack and published by Esquire in April 1975 as "How I became the first person in history to sleep in the Great Pyramid". Perhaps revealingly, the anecdote was cited as one of a pair, the other being a claim made by Ken Kesey, the merry prankster and proponent of LSD. Kesey was set to Egypt on assignment by Rolling Stone in 1974, and claimed to have become "sick unto death" after a few minutes in the King's Chamber.

I'm not clear, having read Sack, exactly where he got the story. He refers to Napoleon and the pyramid, then to Napoleon's death, then adds: "I read in a two-pound book." He may be referring to having read the anecdote, or maybe just to having read an account of the emperor's death, in the mysterious "two-pound book". Either way, he doesn't tell us an author or a title or anything that would allow us to track down his source, if it ever existed in the first place. And Google Books is of no help.

It's also well worth pointing out that the idea that the Great Pyramid possessed strange and supernatural properties was quite widespread in the first half of the 1970s. It was, for example, in these years that the concept of "pyramid power" was widely publicised. This is the idea that pyramid-shaped objects possess beneficial powers, the most widely cited being the ability to preserve foods without refrigeration, and to sharpen razor blades left inside them overnight. Sack was aware of "pyramid power". He references it in his article.