The book doesn't really say why or how Bud's mother died. What we do know is this:
1)Bud was six and Bud's mother was twenty-six when she died.
2)Bud's mother was sick for six days before she died. According to Bud, she didn't suffer.
I said, "I was six years old when it happened, sir. "I don't know why, she was too sick to go to work for six days in a row, then one morning I went into her room and she was dead. But she didn't suffer or nothing, it happened real quick, she didn't even have time to close her eyes, she didn't look like it hurt or nothing."
3)Bud moved to the orphanage when he was six years old, after his mother died.
So, all we can infer from the book is that Bud's mother died from an illness that killed her quickly. What that illness or sickness was, the book never says.