The Yiddish is literally "little grandmother" but the use broadened over time to include males.

The diminutive suffix -ele would be added to make her a little grandmother, i.e. "bubbele."
(That's BUB-schwah-luh, U as in put rather than putt.) Yes, yes, both of them :-) ) The diminutive can be used as a dismissive, somewhat belittling put-down, though paradoxically it also can carry overtones of affection.

Bubbe does mean grandmother, and by extension any older woman, sometimes implying a meddling old woman. It's also the source of a delightful bilingual pun, exploiting the word "Meisse" meaning story, plural "Meissen,' pronounced MICE-en. "Bubbemeissen" are old wives' tales, but if you like you may equally refer to "bubbamycin," the fanciful antibiotic in chicken soup...

Addendum: Sorry, zmjezhd, at least it's only half a mantle... (weak-excuse-for-an-apology-e)