I have been puzzling about that for a week, as I still think bagatella is more likely to have started in Ferrara than Florence, because it turned masculine in Florence at some point there, too: it is Bagatello, in the Strambotto, also an alternate name in Minchiate (along with Papino and Uno). That same spelling and pronunciation, with the -o ending, spread to Lombardy, in the "Pavia" order. But I have had trouble giving what I think is a good argument. I finally have some sort of reply.So, a hypothetical bagatella in Florence, then turned masculine in Bologna at some point - Bagattino (Pedini ms circa 1600), Bagat..
In Ferrara it kept its original name, which goes back to the first generation.
I think it's a linguistic thing. I am not a linguist, but that doesn't stop me. Put it this way. There is a card game with allegorical names for some of the cards. I don't know how many, because it wasn't said until around 20 years after our first confirmed reference to the game, that is, in Boiardo's poem and then the Sermo de Ludo. Let us suppose that one of them is of a sleight of hand artist, and he is called bagatella, for his tricks and the little things he carries around with him. This name either catches on or it is altered to bagatello. I would think that whichever it was, it would be fairly soon after the term was introduced, because once everyone starts using one term, it will be reinforced by continual repetition. Changes do happen in linguistic practice, but they occur over a longer period than just a few decades. In Ferrara we know that the came quite consistently to be called bagatella. So the name stuck. In Florence, however, it didn't stick. It got changed to bagatello, a name it continued to have and which even spread to Milan.
Now if bagatella is the initial word in Florence, and it gets changed to bagatello, that will have to happen fairly quickly, or bagatella will stick. But it's going to take a while for the game to catch on in Florence, enough that it is deemed worthy of export, and probably by the time it reaches that level, the name for the card will be set. Spreading to Ferrara, there is a very small window of time for it to go there with the name bagatella; it has to get there before the game is even established in Florence. Well, yes, it's possible. But there is all the time in the world to go from Ferrara as bagatella and get changed to bagatello in Florence.
There are empirical cases to demonstrate this process in real life. I can think of cases where established terms in England, for example, get changed when they go to America, in spelling or pronunciation. Colour to color, honour to honor. For pronunciation, the city of Birmingham comes to mind, in Alabama, named after the city in England. In all these cases it's the process of rationalization, which tends to happen in new places faster than in the old places.
Then for the other case, where a usage starts in place A, spreads it to place B, then changes in place A but doesn't in place B, where the places in question are autonomous entities, I can think of a few examples, too. Certain communities in the U.S. still use "thee" and "thou", or did, for a long time after these terms stopped being used in England and the rest of the U.S. Likewise "Old Believer" Russian communities in North America still speak 17th or 18th century Russian, whenever they left Russia. Also, some places in Quebec still use antiquated expressions, for example "froque", in instances where in France the usual expression is "manteau" (I know from leaving my coat in a restaurant and the waitress running after me: "Votre froque, monsieur!" But these are changes over a long period in which the two places are in relative isolation. The restaurant was in Chicoutimi; I don't know if the same speech exists in Montreal. From what a French person told me at the youth hostel, about how peculiar the speech was in Chicoutimi, I would think not. While individual Italian city-states did preserve their unique pronunciations and words, they did not in the mid to late 15th century change over the course of just a few decades. Even in Minchiate, for whenever we come to know the terms, "bagatello" is still used, although there are also "Papino" and "Uno." In Bologna, there was the change from "Bagattino" to "Begat." Again, this is a long time after, and probably from the influence of Minchiate, a compromise between "Bagattino" and "Bagatello," taking what is in common between the two words. Moreover, the cases of preservation rather than change when transferring form one place to another involved the resettlement of whole linguistic communities bent on preserving their culture from forces outside, where change is less likely to occur than otherwise. Perhaps you can think of better examples.