Charles Ellicott Commentary 1 Kings 1:47

"And moreover the king`s servants came to bless our lord king David, saying, Thy God make the name of Solomon better than thy name, and make his throne greater than thy throne: and the king bowed himself upon the bed." — 1 Kings 1:47 (ASV)

The king bowed himself, that is, in worship , at once joining in the prayer of his servants, and thanking God for the fulfillment of His promise.