Blanche says this after she has had a long fight with her sister, Kate. The fight is instigated in part because Blanche's date with Frank Murphy has been canceled, as Frank has had an accident. Kate feels that Blanche is too self-centered, and it is clear that Blanche's route out of her sister's house--marriage--seems nowhere in sight. Blanche resolves to move out of the house and find a job.
After she fights with Kate, Blanche begins to fight with Nora, her daughter. Nora tells Blanche she feels unloved, and Blanche responds that she is sorry, but "I am tired of apologizing. After a while it becomes your life's work and it doesn't bring any money into the house" (page 96). Blanche realizes that she has been a weak, apologetic person who has tried to make her way in life by depending on others. She has now resolved to be more independent and to find a job, feather than depending on her sister and her brother-in-law, Jack, who has just had a heart attack. Blanche says, "I've already buried someone I love. Now it's time to bury someone I hate" (page 96). By this, she means that she already buried her husband, and now she wants to bury her old, dependent self and be reborn (metaphorically) as a more independent and active person.