I would not say that the young boy, narrator, in "Araby" is shy. But I can see why you might think so. The entire story occurs within the boy's mind. This kind of introspective narration might tempt you to think that the narrator is shy, introverted or avoiding the outside world. This is not the case. It is simply a story in which the narration is mental. The young boy is a typical adolescent, with the exception of perhaps being of above average intelligence.
You may also think he's shy because it seems like he is intimidated by Mangan's sister and intimidated when talking to girl at the bazaar. To a certain degree, the boy has a natural shyness with Mangan's sister because he has put her up on a pedestal, so he's just nervous. But, when it comes to that final scene, it isn't shyness or nerves that make him leave the bazaar the way that he does. After listening to the trite conversation between this girl and the two young men, the narrator puts it together. He sees that his almost spiritual praise of Mangan's sister was, after all, just a crush and one that would probably result in superficialities like the dialogue he witnessed between the girl and two young men. So, he's not shy for leaving the bazaar without buying something. He realizes (epiphany) that, comparable to the talk between the girl and two guys, he took his own idle small talk with Mangan's sister and raised it, in his mind, to a spiritual romance. And this realization compels him to leave; not shyness.