score:14
Your last quote from Bourrienne seems to be the most correct version. Essentially, the context is that Napoleon held a very high opinion of the East and wanted to organize expeditions at least as far as India. The quote seems to have been said before his expedition to Egypt, and was likely in reference to further eastward expeditions.
Since Bourrienne was such a close contemporary of Napoleon it's probably the best we can get. However, even different versions of Bourrienne's memoirs of Napoleon have different versions and contexts for the quote, so unless someone can find the original version in French we can't completely sure.
Edit: See Pieter Geerkens answer for the original memoir in French. The version I have below appears pretty true to the original, but the original is certainly the better source.
This version of Bourrienne's memoirs from 1901 is the oldest version I've been able to find, and provides a version of the quote similar to your last one on page 60:
At Passeriano, seeing the term of his labors in Europe approach, he first turned his serious attention eastward. There, during long evening walks in the magnificent park, this subject formed a no less interesting than inexhaustible theme of discourse with his favorite generals, aides-de-camp, and myself. "Europe," he would exclaim, "is but a mole-hill: there never have existed mighty empires, there never have occurred great revolutions, save in the East, where, 600,000, 000 of people live, where the cradle of all religions is, the birthplace of all philosophies!" Monge was almost always present at these conversations. That learned man, ardent in mind and heart, falling in with these opinions, excited yet higher enthusiasm in the bold spirit and lively fancy of our General. We all joined in chorus.
Furthermore, he was clearly interested in an expedition to India after he was finished solidifying his control over Egypt, which itself was an expedition mainly of his own design:
Doubtless, the project of the colonization of Egypt was not newβit had been proposed to Louis XV. by the Duke de Choiseuil; but the design had slumbered along with so many others, in the forgetfulness of dusty parchments. revival is entirely due to Bonaparte... A short time before our departure, I asked how long he intended to remain in the East? "A few months, or six years," was the reply; "all depends upon events. I shall colonize the country, and take out artists, workmen of all descriptions, women, actors. We are only twenty-nine; we must be thirty-five. These six years will suffice me, if things succeed, to reach India. Tell all those who talk of your departure that you are going to Brest. Say the same to your own family." I did so.
Upvote:10
To expand on the answer by Giter, here is the original French of de Bourrienne's retelling of that passage (V 2, pp 44) from an 1829 French edition in the NY Public Library:
My take is that Quinn's version sounds like a mis-remembering of de Bourrienne's, a simplified recollection. But it is more difficult to imagine how de Bourrienne's version would arise from the original being Quinn's version.
The complete French for de Bourrienne's Memoires sur Napoleon is available online in its original ten volumes.