1 Kings 1:11 - Joseph Benson’s Commentary on the Old and New Testaments

Nathan spake unto Bath-sheba Who, being private and retired in her apartment, was ignorant of what was done abroad; and who was likely to be most zealous in the cause, and most prevalent with David. To her Nathan was induced to speak, both by his piety, that he might fulfil the will of God declared to him concerning Solomon's succession, 2 Samuel 7:13; and by his prudence, knowing that Adonijah hated him for being the principal instrument of Solomon's advancement. That Adonijah doth reign It seems they were so bold as to proclaim him king.