Given all the evidence of Polish ladies being called Busha in varying locations in the US, it only stands to reason that this came from Poland.
I knew this topic would sooner or later emerge on the PF again (it is one of the most favourite topics here), so it is worthwhile to quote what the more serious Polish-Americans have to say about it:
Here's the link to this website: ampoleagle.com/busia-or-babcia-ongoing-controversy-p4400-125.htm
And here is the most essential part of that article:
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The authoritative multi-volume Słownik Języka Polskiego (dictionary) of Karłowicz, Kryński and Niedźwiedzki (Warsaw, 1905) lists the following forms: babka, babcia, babciutka, babeczka, babusia, babuś, babuchna, babunia, babuńcia, babuleńka and babulinka.The busia version is not among them.
That means that busia is a strictly Polish-American term part of an indigenous Polonian culture like polka music which is unknown in Poland. Nobody knows when, where and why the first American with Polish immigrant roots uttered the word busia. It could have originated as baby talk by someone too young to say babusia, one of the forms listed above. Whatever the case, it somehow caught on and can now be heard from the Eastern Seaboard to the West Coast, from the northern states down into Florida, Texas and the southwest.-----------------------------------------------------------------------------------------------------
In my view, this is a very accurate and competent explanation. Notice that it evokes a rather old dictionary which means that even in the 19th century the word "busia" was unknown in Poland (I also doubt that it was known earlier). If the PF wants to continue to rant about "busia" for ages, that's their choice, but I am sure nothing more could have ever be disclosed on the subject.