Well, I don't think that Ida "Bell" Durham was originally a Durham. My point in listing them the way I did is that it seems that she may have been the matriarch of those Durhams listed and possibly married to that William Frank Durham on that list I found.
Back then you would see certain given names often in families, so I thought that they may be linked to your William Frank Durham, and if so (betting on my theory as correct) she married into the Durhams.
As I said I was trying to confirm her parents. My Robinson ancestors were also buried in that cemetery, and they had a daughter Ada/Ida born about the same time (according to census records). Their names are John Morgan Robinson and Elizabeth Ada Bell. See the potential connection. I'm attempting to make the link.
There could have been multiple Ada/Idas and William Franks back then, but I hoped that you recognized the locale, and may shed some light of the list I gave.
But at least you know now that there are other Durhams of similar names in this area, which could eventually shed light on what you're looking for.
Here are the "William Frank Durhams", currently list on findagrave.
Grave Search Results
Records 1 to 10 (of 10 total matches)
Durham, William Frank 8605748
b. Jul. 25, 1907 d. Nov. 8, 2001 Beulah Thomas Baptist Chu...
Durham, William Frank 72948295
b. 1870 d. Jul. 9, 1944 Tecumseh Cemetery
Durham, William Frank 74824671
b. Jun. 24, 1933 d. Oct. 13, 2005 Dodd Cemetery
Durham, William Franklin 21168824
b. Oct. 9, 1888 d. Jul. 24, 1972 Dement Cemetery
Durham, William Franklin 24074958
b. Apr. 4, 1853 d. Feb. 20, 1918 Fants Grove Baptist Churc...
South Carolina, USA
Durham, William Franklin 28355288
b. Aug. 31, 1832 d. Jan. 13, 1914 Howertons Baptist Church ...
Durham, William Franklin, Jr 28355301
b. Jun. 25, 1870 d. Feb. 22, 1914 Howertons Baptist Church ...
Durham, William Franklin "Will" 35974242
b. Apr. 24, 1898 d. Mar. 29, 1971 Bethlehem Missionary Chur...
Durham, William Franklin "W. F." 64436059
b. unknown d. Jun. 29, 1998 Lawrence County Memorial ...
Durham, William Franklin "Will" 72955580
b. Mar. 15, 1976 d. Jul. 1, 2011 Woodlawn Memorial Park