In a fast pace globalizing world, there is a pressing need for cultivating cross-cultural understanding and empathy in international diplomacy, education training, social discourse. There are already tools available for online cultural training, but they are mainly static and inflexible, which tends to restrain end-users in engaging both on the interaction and transference levels. This generative AI based Adaptive Storytelling methodology (called Cultural Bridge Game as presented in the paper), adds flexible stories with moral decision making to support intercultural communication. The system utilizes Large Language Models (LLMs) and knowledge graphs combined with an ethical scoring engine to create context-sensitive, culture-sensitive narratives that change in response to user choices. Utilizing story-based learning and moral reasoning, the platform fosters empathy and intercultural understanding in an engaging, private context.