“kneeled and bowed down.” This kneeling preceded bowing down to the ground. The two actions, kneeling and then bowing to the ground blended into one act of homage or worship. The common biblical way of bowing down before people or God was to fall to one’s knees and bow the upper body and face to the earth. Also, instead of “kneeled and bowed down,” the text could be translated, “bowed down and worshiped,” with “kneeling” being understood as part of the process of bowing down, and “bowing down” was the act of worship. The same Hebrew verb, shachah (#07812 שָׁחָה), is translated as both “bow down” and “worship;” traditionally “worship” if God is involved and “bow down” if people are involved, but the verb and action are the same, the act of bowing down is the worship. [For more on bowing down, see commentary on 1 Chron. 29:20].
“What can I do for you?” The Hebrew is idiomatic: “What to you?” David recognizes that Bathsheba had some kind of petition.