Not a Polish word.
Please pip, not again. This word is as Polish as mamcia, żońcia, wujcio, stryjcio, stryjeneczka, wujaszek, synuś, wnuś, babusia and babuś. The only difference is that "busia" appears only in several dialects across Poland and is not listed in any mainstream dictionary. It is however listed in several dialectal dictionaries.
And to cool some tempers here - according to [1], the word "babcia" has not been even officially registered in any Polish dictionary
until 1958, since it only appeared (in endearing sense) in the Doroszewski's dictionary[2]. The so-called Warsaw Dictionary[3], does not have such an entry, and only mentions the word "babcia" four times in passing as "ciocio-babcia" or "ciocia-babcia". You may check it yourself using the browser [4]. Certainly no such word exists in [5] - a dictionary of the 16th century Polish - although babka is. There is also no entry for "babcia" in Linde's dictionary[6] (1854-1861), but babka is.
Doroszewski has two separate entries for "baba", one for "babka" and one for "babcia". The latter is defined as "affectionally about mother of father or mother; about old woman". His entry for "babka" has 14 meanings, carefully described.
[1] R. Tokarski: Struktura pola znaczeniowego (studium językoznawcze). Warszawa 1984, s. 137
[2] Słownik języka polskiego pod red. W. Doroszewskiego, 1958 - 1969, doroszewski.pwn.pl
[3] Kryński, Karłowicz, Niedźwiedzki (1900 - 1927) "Słownik języka polskiego", a so-called Warsaw Dictionary
[4] Browser with advanced search capability of multi-volumed Warsaw Dictionary[3] and also other dictionaries, poliqarp.wbl.klf.uw.edu.pl/slownik-warszawski/
[5] S. Bąk, M. R. Mayenowa, F. Pepłowski (eds.). Dictionary of the 16th century Polish. Wrocław - Warszawa, 1966-???? (work in progress)
[6] M. Samuel Bogumił Linde. Dictionary of Polish (2nd edition). Lwów 1854-1861.
I am also bored of repeating the old arguments, so I just only suggest that you google [busia gwara -kenya -uganda] in order to see several entries to dialectal dictionaries - all describing "busia" as "babcia". And then take a look at a map of Poland to see where are those areas where the word "busia" is used in diminutive or hypocoristic form. And just to avoid getting into yet another boring discussion: those areas are NOT Kashubian. Pay attention to Kociewie, Babimojszczyzna, Kramsko, Wijewo, Mazury Wieleńscy, Stara Wiśniewka.
I recently asked my 85 year old ciocia from Silesia about this word. She tells me in all her years she has never heard this word at all.
The former
Lower Silesian dialect is still preserved at Chwalim near Wolsztyn (Zielona Góra) and in the so-called dialect of Rawicz's Chazaks, which includes two villages near Leszno (Brenno and
Wijewo) and about 22 villages near Rawicz. These dialects have survived thanks to the settlement in the past of Silesian population on the border of the Greater Poland and Silesia. Currently those dialects are vanishing.
Wijewo dialect is one of those areas where busia = babka.
But to sweeten up this post, here is a jocular Kashubian text, where the word Busia is used. I hope you like it:
by Zyta Wejer. Nowi Rok - barani skok!Pszede Nowim Rokam je zylwester. A wew zylwestra, to ji wew Niybjesiych só jinsze porzóndki, jak wew codziań. Wew zylwestra Pan Bóg je całki zacharowani, bo łustawja rzónd za rzandam Swojych Amniołóf, bo musi jych fol posłać na ziamnia, cobi piloweli tych małych gzubóf, jak jejych rodziciele jidó balować!
Niechtórne rodziciele psziwjezó Busia, żebi pilowała gzubóf. Ale ledwo tata zez mamó wilyzó zez chałupi, to Busi na drzemka sia weźnie, ji take je jeji pilowanie! Zaś starsze gzubi, chtórne majó mniyć baczanie na sfojych młodszych braciszków ji siostsziczkóf, zacznó patrzyć wew komputer, a małe gzubi brojó, jano sia szaszór robji. Tedi sia nie dziwujta, że Pan Bóg sóm siedzi na zydlu, rance ma łoperte ło baki, ji szandyruje tych amniołóf, żebi choc łóne mniałi baczanie na ty zafajdane malusziska. Jano że majó pilować fszitkych, a niy jano tych, co rano mówjyli: "Amniele Bożi, Stróżu mój, ti zawdy pszi mnie stój!". Niy, niy, Pan Bóg tak nie rachuluje.