1 Kings 1:31-33

Kings 1:31-33King James Version (KJV)
31 Then Bathsheba bowed with her face to the earth, and did reverence to the king, and said, Let my lord king David live for ever.
32 And king David said, Call me Zadok the priest, and Nathan the prophet, and Benaiah the son of Jehoiada. And they came before the king.
33 The king also said unto them, Take with you the servants of your lord, and cause Solomon my son to ride upon mine own mule, and bring him down to Gihon:
An American English Bible
With Old Testament based on the Greek Septuagint

31 Then BathSheba bowed low with her face to the ground, and said: 'May my lord King David live through the ages.'
32 Next, King David said: 'Call SaDoc the Priest, Nathan the Prophet, and BenaiJah (the son of JehoiAda) to me.'
So they came in and stood before the king, 33 and the king said to them: 'Take my servants with you and mount my son Solomon on my personal mule, then take him to GiOn.

These are my thoughts, please share yours.

31 This was the wife of David and mother of Solomon. This was the woman David had adultery with and tried to cover up by murder. She is not worshiping him but just showing him respect, it is highly unlikely that this would have been more then sometime of kneel, it would not have been a face down bow as done for worship of the Lord at that time. David would not live forever but his line would continue thru Christ who reigns forever and longer. David would die but Christ would rise from death after which His reign started.

32 The priest carried God’s law and the prophet carried God’s word, he called them to see what God had for him to do, Benaiah was a leader in his military; these men represented the men that remained loyal to David being king. When fight the fight of faith God will send us those who are loyal even though sometimes those closest to us may become our enemies, it was David’s own son causing the problems.

33 This would play a very important part in the Passion Week where Jesus rode thru town on a donkey. This was to show the kingship, Jesus did this to show He is King and David had this done with Solomon to show he was to be the next king.