I grew up calling my grandmother Babusz (pronounced Boboosh)
Female words usually end with an a so it wouldn't be Babusz, that sounds sort of like a man. Babusia was probably what y'all were using initially and it became Americanized into Boboosh.
Dziadzia is a baby version of the word dziadek, it's simply easier for babies to say that before they learn to talk.
Ciocia is the correct term for aunt.
WHile I was growing up I was taught Busia and Dziadzia. My family hailed from Bydgoszcz Poland, settled in Bay City Michigan in 1920's.
Oh boy, here we go again, another busia - the American-Polish term no one in Poland seems to know... LOL
There's no "busia" - there's buzia which means kiss and there's babcia which means grandmother... There's also
babusia another Slavic endearing term for grandmother.
This threads explains it in great lengths.
Slow download but the third word you hear is "ciocia" (aunt).
apronus.com/polishsounds/cma_lac_ciocia!s.mp3
Saw this on a different thread and copied it but forgot to copy the URL, if I find it I'll post it too.
A nice characteristic of Polish language is diversity of diminutives that may be created for almost any noun. "Babcia" is diminutive itself, the formal form, almost not used, being "babka". There are a few other diminutives for "babcia": "babunia", "babusia", and shortened forms: "bunia", "busia". Maybe the last one is "busha".