SeekingMichigan.org death certificate online shows Zilpha Dixon Bates died in Tuscola County, Michigan, in 1908, with burial in Essex Center, Vermont.
George Bates is her son and married and died in Tuscola County. There is indeed another George Bates who is a son of Allen Bates. Allen Bates is also buried in Vermont.
Research shows several family trees on Ancestry have mixed the two George Bates. Here is some information that we hope will be helpful.
Zilpha Bates, b. June 3, 1829, Vermont, d. Nov 20, 1908 in Almer twp (probably living with her son George Bates), father Solomon Dixon, mother Poley Wickom, burial in Essex Center, Vermont on 25 Nov 1908.
I do find George and Zilpha Bates in the 1870 census in Essex, Chittenden Co, Vermont with children Harriet, George, and Sarah.
In 1900, George Bates, b. Feb 1861, wife Ella, b. Jun 1865, dau Vera b. Sep 1886, and Sarah b. May 1889, in Almer twp, Tuscola County.
5 Oct 1882, Caro
George R Bates, 21y, residence Almer twp, b. Vermont
Ella Parsell, 17y, residence Almer twp, b. Michigan
By Alex Reynick, JP
Witnesses, Frank Taylor and Edith Macomber
George R Bates
Michigan, Death Certificates, 1921-1952 birth: 14 February 1861 Vermont
death: 30 March 1925 Almer, Tuscola, Michigan, United States
father: George Bates
Ella A Bates
Michigan, Death Certificates, 1921-1952 birth: 3 June 1865 Tuscola, Michigan
death: 7 May 1952 Caro, Tuscola, Michigan, United States
father: Franklin Parsell
mother: Patience Dickinson
FindaGrave has photo of grave marker which would not copy here
Mountain View Cemetery
Zilpha Bates (1831 - ____)*
Sarah Bates Dutton (1865 - 1892)
Marriage record, Essex, Vermont
24 Oct 1852
By Rev. John D Sands