Bowing or not bowing is a no-win thing for American presidents. Usually the bend down a little from the waist, which isn’t hard because Elizabeth II was only 5’3” or 5’4” (same as Hillary Clinton).
I imagine she gave the Obama speeches to Charles, as a fellow traveller he will appreciate them more.
If you think the big white courtesy phone is busy now, wait until Obama and the Clintons go hob-nobbing with Charles and Camilla.
At that time, I will regurgitate for a world record three hundred and eighty nine days.