Hi cathy m,
I wish you very well with your research and I hope that you do finally find Mary MORRIS. The information and advice from corisande seems excellent. Do let us know if you find Mary.
As there is a Bohermore in Co Galway, I think I'd persevere with that before checking out Bothermore. They do look quite similar but I wonder about pronunciation?
Anyway, best of luck.
Kind regards,
JAP