I looked into your previous postings for more information, but far to many postings to look. There isn't enough information posted here to properly search for clues. (Sorry, to much time in investigations).
I'm "assuming" you have the bible and your information is from an inscription? If so, how exactly does it read? Does it appear this Mrs. A.G. W. was living in Bannock County, or it was presented in Bannock County? Or did it read, "December 25, 1899, Bannock County," which would more likely be where Alice Canfield was living? Look closely at the letters, could the "A" be an "H," with the top joined? Or, a "G?"
Mrs. A.G. Walworth. Those initials may be hers or her husbands. She may have been a friend of the family from almost anywhere, or lived in Bannock County. If she lived in Bannock County...
...Where was Alice living in 1899? I do not find an Alice Canfield in Idaho in the 1900 Census. There were 48 Alice Canfield in the 1900 Census (to many to guess). If you have her DOB, it might help to post it to see her age in 1899/the 1900 Census. The 1900 Census would show where she was living at that time. Where was Alice born and lived up to 1899? That might help show where this A.G. W. may have known her; or her family. Knowing the correct Alice Canfield can identify her parents and where they were born and living prior to 1899.
I do find an Alice G. Walworth, born Feb 1867 in Louisiana, living in Natchez, Mississippi in the 1900 Census. She was living as Sister-in-law to Clara Walworth, "possibly" married to J.P. Walworth, born April 1857 in Mississippi. Alice was born in LA to father born in England, mother in Pennsylvania. You identified Lineage to the British Isles, could she have been related to Alice Canfield, thus the similarity in name?
I find a Harry G Walworth, as transcribed, in the 1900 Census, the name was corrected by someone to a Harry A. Walworth. Married to Florence, living in Battle Creek Michigan, born in Wisconsin in Mar 1867.