It doesn't mean 'bitch' (that would be "tispe"), though in many dialects it's only used about women in the same way that word is. The literal meaning is just '(grown-up) woman'. In some dialects, it's still just used to mean 'wife' or '(old) woman' without anything negative, though in modern times the negative connotations have spread so it's used less and less like that. But it shows up in fairy tales and kids stories ( https://no.wikipedia.org/wiki/Kjerringa_som_ble_s%C3%A5_lita... ) and songs; you'd never see the word "bitch" used about women in English in material meant for children …
On behalf of Norwegian language users, thanks for the clarification. You explanation seems to be extremely precise.
(My qualifications: I've lived permanently in Norway since before 2000, I speak a Norwegian dialect and pass as a Norwegian all the time. I'm also married to a Norwegian woman so I kind of know the nuances. For Norwegians here: in my family it stops at "kone" even though by the dialect I speak it should rather be pronounced as "kåne" : ).
Yes, it depends on where in Norway you are, and the context, but if someone yelled "kjerring" somewhere around Oslo, the best translation would be "bitch".
If you disagree, we'll have to duke it out with Holmgang. ;)