A precursor to this idea was the Mirror Glass, credited to Hofzinser (Barton Whaley cites an 1872 creation date in The Encyclopedic Dictionary of Magic, 1989, p. 609).
Another related item is the “Transparent Egg Bag”, which employed a different method (a see-through mesh front with a black backing, and a secret compartment in the back panel concealed by the Black Art principle). This surfaced at least as early as 1923. A version was marketed by Conradi circa 1924 (see a mention of it in The Sphinx, Vol. 23 No. 5, July 1924, p. 158). The trick's invention was claimed by the Austrian manipulator, Larette; see The Linking Ring, Vol. 9 No. 7, Sep. 1929, p. 728.
The first clear change bag on the scene wasn't a bag at all; it was a glass fishbowl. It was identical in construction, concept and application to the modern clear change bag. The only difference was that instead of flimsy plastic, it was made of hard glass (the clear divider, however, was still a thin plastic sheet). This was the invention of U.F. Grant, and included in his “$500 Letter Reading Test” from Brain Busters, 1945, n.p. (“Trick No. 4”).
Robert Harbin developed the same concept as Grant, applying it to a clear plastic bag, creating what we now think of as a clear change bag, constructed from cellophane, and published it under the title “Visible-Invisible Change Bag” in Abracadabra, Vol. 9, No. 227, June 3, 1950, p. 293. (It is worth mentioning that Harbin's version had a feature that is missing from almost all of the later reinventions.) Other than a brief favorable mention in Dariel Fitzkee's literary review column in Genii, Vol. 14 No. 12, Aug. 1950, p. 430, the Harbin bag seems to have gone unnoticed. The description from Abra was included in a later book compilation, Habincadabra, 2005, p. 133.
In The New Phoenix No. 319, Nov. 1954, p. 85, Jay Marshall writes that “Homer Hulse mentioned a transparent change bag he intends to market.” There does not appear to be any evidence that he ever did.
In March 1958, Tannen's began advertising “The Visible Prediction,” the clear change bag with no attribution. That same year, this was imported back to England by Harry Stanley, who added a routine using the prop by Maurice Fogel called “The Eternal Triangle”, which is presumably why Fogel is sometimes credited with having invented the item.
Perhaps the terse ad copy was too oblique, because the prop was still largely unknown when in The Linking Ring, Vol. 41 No. 1, Mar. 1961, p. 67, the “Transparent Changing Bag” was offered by Adolph H. Humphreys and praised as a useful new idea by Parade editor, Eddie Clever.
Circa 1960, U. F. Grant came back into the fold a full fifteen years after his original clear change fishbowl and marketed a “Transparent Egg Bag” (credited to Jack Chanin) and a “Transparent Dove Bag”. During that decade, he also sold a “Transparent Change-Bag”. The earliest ad seems to be in Genii, Vol. 31 No. 2, Oct. 1966, p. 99. The ad is for Morcom's Enterprises, but the title and price of the prop ($3) make it almost surely Grant's. It is advertised by Grant in Genii, Vol. 31 No. 6, Feb. 1967, p. 237. Although it is usually referenced as having been released closer to 1960, this is probably due to a conflation of the prior “transparent” bags and this one.
At any rate, in modern times the credit, when it's given at all, is most often given to Grant alone, but the true credit belongs clearly to both Grant and Harbin.
(Above history researched by Max Maven)