The central conflict of the story "Miss Bill" stems from the main character's inability to live in her "here and now". Her dire circumstances, her loneliness, and her inability to connect with he world, make her awkward and detached from reality. The way that she deals with life is by going to the Paris gardens and watching people. Along the way, she concocts stories about the people that she sees, and feels closer to that world which she has created in her mind.
The characterization in the story "Miss Brill" comes from a third person narrator, limited (knows only Miss Brill's thoughts, motivations, feelings) and subjective (aware of and commenting on psychological characterization and on events). This type of characterization unveils for the reader what exactly takes place in Miss Brill's mind and feelings as she develops the stories about her experience at the concert in the Paris garden.
The characterization by the subjective narrator in close proximity to the character and events describes Miss Brill's loneliness and a lack of human connection as having caused her to create a new reality of her own: she creates one in which everyone she sees is part of a huge stage production: "How she loved sitting here, watching it all! It was like a play. It was exactly like a play." She feels as if she and everyone are actors in a big, life-sized play: "An actress!" ... "Yes, I have been an actress for a long time." This is the only way that Miss Brill connects with humanity.
Because the characterization is provided by the narration of a closely proximal, subjective narrator who comments liberally on Miss Brill's traits, feelings, thoughts, actions and motivatives, the reader really gets to know the main character, Miss Brill, and understand how she is and understand that her characterization is what sets up, develops and brings to a climax the central conflict.