There is evidence to suggest that the two-handed shift -– or a related move -– has been in use much longer than the first detailed instructions would suggest, and even then only in card cheating contexts rather than as a conjuring technique. In the anonymous Liber Vagatorum, c. 1512, p. 47 of the Hotten translation, the author discusses cheating, and mentions how the cards are “cut one for the other.” This tantalizing passage might be an early description of the pass, but ultimately it's too vague to be certain.
Over a century later, Charles Cotton described a tabled pass in The Compleat Gamester, 1674, p. 118. There were no technical details provided; the gambler is merely told to “use their hand so dexterously as not to put the top in the bottom, but nimbly place where it was before.” Pierre Ange Goudar next mentioned how cheaters “jump the cut, to put the cards in the same position,” in L’Histoire des Grecs ou de ceux qui corrigent la fortune au jeu, 1757, p. 7 of the second edition. On p. 24 of the same book, Goudar describes a lady cheat, Madame S***, who was “passing the cut…like a flash.”
The first description to explain the mechanics of the move appears in Gabriel Mailhol's Le Philosophe Nègre et Les Secrets Des Grecs, 1764, p. 150. The workings of the move are woven into a story between an experienced sharper named Dioméde and the narrator. Dioméde explains how the narrator was cheated with the pivot cut (pass). Interestingly, while the “classic” pass is known as a top-to-bottom shift –- with the bottom-to-top style considered a later development -– this early description suggests the opposite is true. In Mailhol's technique, the left fingers move the bottom half to the top. For more information on bottom-to-top passes, please see Herrmann Pass.
The earliest instruction in the context of conjuring appears in Edme-Gilles Guyot's Nouvelles Recreations Physiques et Mathematiques, 1769, p. 1 of the Hugard translation (unpublished).
The riffle and dribble actions were later introduced as ways to psychologically cover the shifting packets. Using a riffling action and sound to cover the pass was in use by card cheats in the mid-nineteenth century. Jonathan Harrington Green mentions this ruse in Gamblers' Tricks with Cards, Exposed and Explained, 1859, p. 98. It is unclear from the description whether the riffling was performed within the action of the pass itself, or whether the cheat would riffle before and/or after the pass to help dull the other players' suspicions about movement and sounds coming from the cards. This latter approach was adopted by James Elliott, who popularized the idea in Elliott's Last Legacy, 1923, p. 129. The dribble cover was introduced by a magician who, going by the name Denver, published it in The Magic Mirror, Vol. 3 No. 7, July 1911, p. 50.
For further reading, please see Kurt Volkmann's article, “The Origin of the Shift,” in The Sphinx, Vol. 51 No. 1, Mar. 1952, p. 24; reprinted in Prolix, No. 4, Aug. 2008, p. 237.