In the context of ancient Israel, Bathsheba's gesture of bowing and prostrating herself before King David is a profound act of respect and submission. It signifies her acknowledgment of his authority and her loyalty to him as the reigning monarch. The phrase "May my lord King David live forever" is a traditional expression of loyalty and reverence, not meant literally, but as a way to express her wish for his enduring legacy and the stability of his reign.
This moment is significant in the narrative of 1 Kings, as it occurs during a time of political tension and uncertainty about the succession of the throne. Bathsheba's actions and words are part of a larger effort to secure the rightful succession of her son Solomon to the throne, as promised by David. Her respectful approach to David not only honors him but also strategically positions her to remind him of his promise regarding Solomon's kingship. This scene highlights the importance of loyalty, respect, and the fulfillment of promises in maintaining the stability and continuity of leadership in Israel.