Buba is a relatively common “name” that some women here use between each other (besides being an old/dialect word for a bug). F.e. one girl from my primary school, a Lyubomira, was shortened to Buba (Bube in vocative; though now that I say it, it does make some sense about using it for women). And, of course, Bobby is a common shortening for Boris(lav). Still, maybe there is some archaic root whose meaning we’ve lost with time?
Edit: Or, yes, it could just be a parent-baby-talk thing.