Out of the Dust by Karen Hesse is a novel, so it is not a true story in the sense that Billie Jo and her family really existed. They did not. They are fictional characters, and the events of their lives are fictional as well.
That said, though, there are many, many elements of Out of the Dust that are historical. The novel is set in the 1930s in Oklahoma. These are the years of the “Dust Bowl.” A severe drought hit the middle part of the United States, and the book accurately describes the conditions of this drought. The dust storms, the failing crops, the dying animals, and the dirt that seeps into every part of people's houses are all true to life. People who lived in Oklahoma in the 1930s actually did experience these trials.
The novel also accurately depicts the migrations of the period. People moved from their homes in droves, seeking work and a better life. Like the family of Billie Jo's friend or the family that stayed at the school as they passed through town, these migrants wanted to get out of the dust and dirt and find some normalcy. Unfortunately, since the entire country was experiencing the effects of the Great Depression, most of these migrants did not find what they were looking for.
The effects of the Great Depression are also realistically portrayed in Out of the Dust. Billie Jo's family, like most families of the era, had to survive on little or no money. Even the most basic necessities like food and clothing became scarce. The government offered aid to those in need, as we read in the novel, and this helped some. Families that had a little more also shared with families that had nothing, as we see Billie Jo's mother (and Billie Jo herself) doing. People did their best to help others survive, even though they, too, were suffering.
While the plot and characters of Out of the Dust are fictional, then, the story contains many elements of truth and an accurate picture of life during the 1930s.