Albert Barnes Commentary 1 Kings 1:14

"Behold, while thou yet talkest there with the king, I also will come in after thee, and confirm thy words." — 1 Kings 1:14 (ASV)

Confirm your words - "Establish" them, by giving a second testimony. Nathan thinks it best to move David’s affections first through Bath-sheba, before he comes in to discuss the matter as one of state policy and to take the king’s orders on it.