I would offer a word of advice to those searching for the identity of biological mothers not to discount the possibility that the adoptive mother might have adopted a child from another family member.
My own maternal grandfather was adopted by a woman who always said that she had obtained my grandfather shortly after his birth in 1913 from an orphanage. She also claimed that she adopted the child after her own child had died at birth and that she was unable to have further children of her own. Despite the lack of a blood-relationship, I knew this woman as my great-grandmother growing up and I included her in my family tree and thus knew the identity of her ancestral families.
You can imagine the surprise when my mother and I underwent autosomal testing and discovered multiple DNA matches with persons who were descendants of the same people who were the ancestors of the adoptive mother. We also learned through a cemetery visit that the child of the adoptive mother that had died was born AFTER the adoption of my grandfather.
Through a process of elimination I was finally able to determine the identity of the biological mother, a first cousin who lived a few houses away from the adoptive mother and who would have been 17 when the baby was born. Everyone carried the secret to their graves and but for DNA testing, none of this would have ever been discovered!