While I ordinarily agree about not bowing, I think I would make an exception in the case of the Queen of England. A bow would not be subservience, but simply giving this woman the respect which is her due. Again, she is the one and only exception to the rule.
I think an oblique head bow is one thing, but closed-eye perpendicular head bow is too much, and a waist bow is out of the question for an American. Trump often inclines his head obliquely with a nod and smile when meeting people, as a show of welcome.
Here he is with Trudette:

And here he is with Hitlerette:

With a U.S. veteran, Lou Dorfman:

But this one didn't get a head bow:

Nope. Not this time, either:
