The Secret Life of Bees is certainly a particularly "American" story. There are so many reasons for this, it is difficult to know where to begin.
First, the issue of racism is a prominent issue in the United States, so that alone makes this an American story. The idea of transcending racism is a theme of the novel, and for African-Americans, this is part of the "American Dream." Notice that Rosaleen gets to vote at the end of the story, a symbol of all that African-Americans had been deprived of historically. Notice also that Lily manages to conquer her own racism by the end of the book, as has June.
Second, the novel is firmly placed in American literature by virtue of the plot elements that are similar to those of Huckleberry Finn, one of the greatest American novels ever written. In Huckleberry Finn, Huck and Jim run away for the sake of their respective "freedoms," Huck to get away from "civilization" and Jim, to find freedom from slavery. What do Lily and Rosaleen do? Lily is running away from the unreasonable discipline imposed by her father, and Rosaleen is looking for the freedom that voting represents for her. There are other elements that evoke Huckleberry Finn, and you might want to look for more.
Third, the theme of freedom is a powerful theme in American literature, something Americans have been grappling with since the country's founding. What other great books in American literature explore this theme?
Fourth, the idea that religion can offer solutions to our problems has become an important idea in American literature and politics. Americans are more religious than people of many other countries, perhaps because we began with religious groups who were trying to be free to practice their own religions. Notice that Lily and Rosaleen find peace and happiness when they become part of a religious practice that is not an "approved" religion.
There are no doubt many other aspects of The Secret Life of Bees that make it an American novel, but these should certainly be enough to get you started.