Online content moderators enforce rules on text-based platforms, often using punitive measures like removing content or banning users. However, such platforms continue to struggle with conflictual and uncivil discussions that hinder meaningful exchanges and strain intergroup relations. While online moderation practices are limited, conflict management literature offers strategies to prevent and manage conflict, though their effectiveness in anonymous, text-based settings remains underexplored. Our study addresses this gap through interviews with 22 dispute resolution professionals to explore (a) how they apply conflict management strategies in online discussions and (b) what online moderators can learn from these approaches. We validated our findings through a focus group with moderators from a major Dutch news platform. Our inductive analysis led to the "Bridging Model," which outlines four key conflict management strategies: surveying the scene, laying the foundation for understanding, building social connections, and constructing arches of understanding. We identified challenges moderators face, particularly in fostering social connections between users—an essential yet underused approach that could transform conflictual discussions into opportunities for resolution. This study contributes to content moderation literature by questioning its reliance on punitive actions and emphasizing the potential of conflict management strategies. It also extends conflict management scholarship by applying its principles to online discussions, a critical and evolving site of societal conflict.