1 Kings 1:14

Behold, while thou yet talkest there with the king, I also will come in after thee, and confirm thy words.

Nathan arranged with Bathsheba that she would speak to David first and he would come in after her to confirm what she had told the king, and this belonged to their united effort to secure Solomon's succession. Their coordinated approach was to alert David that Adonijah was claiming the throne and to bring the threat of his rebellion to the king's attention. It was also to remind David that Solomon was to succeed him and to move him to act by having Solomon made king.