I think the reader can most likely conclude that the speaker: Recognizes and respects her grandmother's social position
During her bath, the narrator slowly understands her Grandmother position as she grew older. If we pay attention to our society, we will see that the elderly keep losing power as they got older. They used to be listened by their children but after a certain age, the position is reserved. The children took more power over their old parents.
Hope this helps :)
