According to Paula McLain, who researched Hemingway's life extensively for her novel about his first wife Hadley, Jack "Bumby" Hemingway admired his father and valued his time spent with him. He lived with his mother and her second husband but visited his father often. It seemed that of all three of Hemingway's sons, Bumby had the easiest time relating with his father. She surmises that this might be because Bumby's mother was favored by Hemingway more than the other boys' mother even though they divorced.
Other writers note that Bumby looked very much like his father and followed his father's lead in military duty. He appeared to be very much interested in his father's life, even writing a memoir specifically about his life with his father.