Grant wrote this for her daughter Millie, who was six weeks old at the time.
We asked Amy in a 2013 interview
what Millie - then 23 years old - thinks of the song. Amy replied: "I think she just says, 'This is the song inspired by me.'" She added: "When they were younger, they traveled with me on the bus. I mean, as they got older, I had to take a tutor until they were old enough to not want to travel as much as I did. But I didn't ever force my children to have any kind of emotional attachment to the music I made, because I knew that they would find the music that they loved, and I didn't ever want them to feel pressured. I jokingly have said, "Oh, I'm so glad I heard 'Baby, Baby' in an elevator the other day, because it's helping defray the cost of your college education." [Laughing] But it's just like, 'Well, that's what Mom does.'"