In chapter 34 of the Bakemonogatari manga, Kanbaru talks about her past. When she discusses her living situation after the death of her parents, she says:
I was bullied at the school I transferred to, simply put. I still have an accent now, but it was a lot worse back then. I had a lot of problems myself, but my head was filled with my parents.
What accent is she referring to? While I can find a mention of Kagenui having a Kansai accent, I can't find anything for Kanbaru at all, both explicitly in regards to her accent and in regards to where she was living before her parents died, which might provide some information here.