When you post a question, you should include any location for b, m, d that you are aware of - including Country, city, town as it makes it easier for someone to help.
PS in 1940 this Lenora I Bedford is also listed as living with her mother in CA???
This woman Lenora Irene Woodside, father George Bedford, mother Bessie Jumper is a possibility, but you would need to confirm by marriage or death certs. The death records or Lenora Irene, Kenneth Sr. and Kenneth jr are all listed on familysearch.org.
https://familysearch.org/ You might want to get the actual certificates to see if you can prove the connection.
U S Census, 1940 Ward 1, Bakersfield, Judicial Township 3, Kern, CA
head Kenneth Woodside M 33 KS
wife Irene Woodside F 29 CA
son Kenneth Woodside M 13 NE
California, Death Index, 1940-1997
Citing this Record "California, Death Index, 1940-1997," index, FamilySearch (https://familysearch.org/pal:/MM9.1.1/VPNV-BGR
Lenora Irene Woodside
Death 15 Apr 1988 Riverside, CA
birth date: 21 Jun 1912 Wyoming
father: Bedford mother: Jumper
U S Census, 1940 Tract 461, Covina, El Monte Judicial Township, Los Angeles, CA
Citing this Record "United States Census, 1940," index and images, FamilySearch (https://familysearch.org/pal:/MM9.1.1/K97F-CR5
head Lenora I Bedford F 27 WY
mother Bessie I Bedford F 57 KS
U S Census, 1930 Covina, Los Angeles, CA
Citing this Record "United States Census, 1930," index and images, FamilySearch (https://familysearch.org/pal:/MM9.1.1/XCFN-7B3
head George Bedford M 56 KS
wife Bessie Bedford F 45 KS
son John Bedford M 18 WY
dau Lenora Bedford F 16 WY