Your wrote the adoption took place in Miami County, Kansas.

I searched through births, deaths and marriages in the records available on the Miami County government website:

http://www.miamicountyks.org/260/Genealogy-Records

I don't find anything that pertains to Bessie or her biological parents.

The 1900 Miami County, KS, census enumeration lists a BessieWILLIAMS as the daughter of Charles H. and Anna WILLIAMS with her birth given as February 1896 in Kansas. The mother lists giving birth to two children and still had two children living. From this 1900 census it appears children Bessie and Leah, born July 1899, are the biological children of this Charles and Anna, or were at least represented as being their biological children.

Beth
not related