old bag vs unpleasant woman

old bag and unpleasant woman both are nouns.

Word	Noun	Adjective	Verb	Adverb
old bag	Yes	No	No	No
unpleasant woman	Yes	No	No	No

As nouns, unpleasant woman is a hypernym of old bag; that is, unpleasant woman is a word with a broader meaning than old bag:

Other hypernyms of old bag include disagreeable woman.

old bag (noun)	unpleasant woman (noun)
an ugly or ill-tempered woman	a woman who is an unpleasant person