It is hard to know exactly what Della might be thinking at that point in the story. That sequence is the first seven sentences of the story. As the reader learns a little bit more about Della and her feelings for Jim, the reader can begin contemplating what Della was feeling in the beginning of the story.
I believe that a main feeling of Della's was disappointment. Not disappointment in Jim and his job, but I think Della felt disappointed in herself. The text says that she had been carefully saving by trying to shop in a thrifty manner.
"Pennies saved one and two at a time by bulldozing the grocer and the vegetable man and the butcher until one's cheeks burned with the silent imputation of parsimony that such close dealing implied."
Despite all of her hard work and diligent shopping, she had only managed to save $1.87. She feels disappointment in herself, because she wants to show Jim that he is worth so much more.
I think Della also feels a bit dumbfounded. I think that is why she counted the money three times. Della simply can't believe that all of her efforts have amounted to only such a small amount. I can almost hear her thinking "$1.87? Surely that can't be right."