John Gill Commentary 1 Kings 1:16

"And Bath-sheba bowed, and did obeisance unto the king. And the king said, What wouldest thou?" — 1 Kings 1:16 (ASV)

And Bathsheba bowed, and did obeisance to the king
Not only as being her husband, but her sovereign; and this behaviour might intimate, that she had something to say to him, and more than to inquire of his health:

and the king said, would you ?
what have you to say to me? or to ask of me? what is your will and pleasure, or your errand to me?