I am not related to your families at all, but I do live in Nova Scotia. I just want to say I agree with your conclusion about your BIERCE/BEARSE names not living here. There were never any such names (to my knowledge) in NS, or for that matter, anywhere in Canada to speak of. Doing a quick look-up using - www.canada411.com - shows only 3 BEARSE in Canada, all in Ontario, and NO spellings of BIERCE at all.
I agree you will have more luck searching in CT, RI, MA, and NY areas. Good luck.