There's actually very little evidence that anyone in Italy actually knew anything about JS Bach. Although the New Grove (the standard encyclopedia for music) asserts that Bach's keyboard music was printed in Italy by 1750 I can't find any evidence of this (that's from a bibliography of printed music related to Bach, searching for the year "17" and restricting the language to Italian. Notice that JS Bach is never on the author list, and he isn't included in any of the edited collections on that list that I've been able to find).

I think the best place to look for Bach's international reputation is Charles Burney. Though an Englishman, Burney deliberately made an attempt to catalogue both the musicians and cultural attitudes toward music in all the major European states. If anyone in the mid-eighternth century outside of Germany knows who Bach is, it's this guy. Here's what he has to say in a book on Germany's music from 1775:

Besides many excellent compositions for the church, this author produced Ricercari, consisting of preludes, fugues, upon two, three and four subjects; in Modo recto & contrario and in every one of the twenty-four keys. All the present organ-players of Germany are formed upon his school, as most of those on the harpsichord, clavichord and piano forte are upon that of his son, the admirable Carl. Phil. Emanuel Bach ; so long known by the name of Bach of Berlin, but now music-director at Hamburg. (83)

So perhaps the most musically learned man on the continent essentially regards Bach as a great organist, a clever composer of fugues, and a masterful pedagogue. But of course, Burney only knows this because he went to Germany, read closely the writings of German critics like Quantz and Marpurg, and listened to the stories of German musicians. He is essentially the only international voice to talk about Bach, and he does so by regurgitating German writers.

As far as we can tell, Bach in his lifetime was mostly a relatively obscure, provincial musician. He did not write in the genres that mattered to Italians, like opera. So much of his work was based on practices of the Luthran church, so it is no wonder that the Catholics of Italy would not have encountered his sacred works. His harpsichord works were published, but not circulated outside of German-speaking lands, apparently. If you asked an Italian about Bach, they would most likely assume you were talking about his son JC (who was a very successful opera composer). They knew essentially nothing about JS.

Bach's reputation begins to surge with the writings of critics in and around Berlin in the last decades of the eighteenth century. Including writers like Marpurg and Kirnberger, as well as important connoisseurs like the Baron von Swieten in Austria. From these writers, Bach's music entered the ears of Mozart and Beethoven (the latter probably also because of a continuing German tradition of raising keyboard players on Bach's music, as Burney alludes to), and, later, Mendelssohn. And it is Mendelssohn who spearheads the Bach revival in the early 19th century, which cemented JS as the figure we know him as today.