Such a mystery, she really does seem to have vanished, but with no burial record either I cant help but come back to the thought that she wasn't a Bambrough,Bell or Barker when she died, otherwise you would have found
some record.
Have you ruled out all possible marriages that could be her third marriage ? If not, try cross referencing all Mary/Mary Ann/Ann Bambrough (or even all female Bambrough) marriages in Newcastle after April 1901 with the death records for people with that married surname born 1846,died after the marriage date.
even longer shot would be, search probate records for all Mary Ann's who died in Newcastle between 1901-1910 (or beyond), and look for any name/address within the record that tallies with something you already know.
Just for my curiosity, where did Mary Ann marry William Bell, Scotland or Newcastle ?
Good luck, and keep us posted. I love a mystery, so I'll keep looking