Head bobbing in budgies is usually totally normal behavior. Male budgies especially do this as a sign of contentment, excitement, or even as a mating display. The fact that he's doing it when he sees you or hears sounds suggests he's reacting to stimuli and probably just happy to have your attention. It's basically their way of saying "hey, I'm here and I'm feeling good about things."
Since he's eating fine and seems otherwise happy, you don't need to worry. The one-week timeline isn't concerning either - budgies can pick up new behaviors or quirks pretty randomly. Just keep an eye out for any other changes like ruffled feathers, discharge from his eyes or nose, difficulty breathing, or changes in appetite. If any of that shows up, then you'd want to get him checked out. But solo head bobbing? That's just normal budgie personality stuff.