O. Henry is considered a master of the short story, and this excerpt tells you why. His very first paragraph tells you something about a main character and about the conflict.
Parsimony, or penny pinching, is generally considered an undesirable trait (or was in Henry's time). A young married woman such as Della would be responsible for shopping and cooking, and she would receive an allowance from her husband for food. The local merchants have no reason to think that Della lacks money. Instead, they would believe that she's driving a hard bargain ("bulldozing") to be unpleasant. They would naturally impute, or ascribe to her, this stinginess and disrespect. However, they wouldn't say that out loud to a lady, hence their silence.
Beneath it, however, Della's "cheeks burned." She is embarrassed by having to do what she's doing, and yet she has done it for some time and continues to do it. Shame is another quality that is viewed differently today. It was quite powerful in earlier times. Henry is telling us that she has motivation strong enough to offset her shame, and that will help drive the story.