I can't remember exactly, but I think there was some kind of light story element to "The New Way Things Work"
Edit: just noticed the bit about not reliant on pictures, that rules that one out. I recommend it regardless, but maybe not for the exact use-case you're describing
The various Way things Work and similar books have always had a light bit of story, but not really anything thats properly bedtime appropriate, emphasis on the "light." Its generally a bit of flavor text at the start of a section, describing the journey the Mammoth and its companion went on as they move through the books, with things such as the "Digital Domain"
Edit: just noticed the bit about not reliant on pictures, that rules that one out. I recommend it regardless, but maybe not for the exact use-case you're describing