The bent woman is merely a nickname for a shaman, or priestess, who lives at the seal camp where Miyax spends her childhood. During the Bladder Feast, she dances in costume, and later, she tells Miyax about i'noGo tieds, or totems of animal spirits. She pops up again, awhile later, when Miyax sees her "putting the spirit of the whale in her i'noGo tied" (2.18).
Although the bent woman is not a very important character plot-wise, she represents something very important in the novel: Eskimo culture. The bent woman is a traditional Eskimo, through and through. Miyax, becoming more and more of a traditional Eskimo with each passing page recalls the bent woman, and sings her healing song as she tends to Kapu's wounds in Part 3.