Intergenerational co-creation using technology between grandparents and grandchildren can be challenging due to differences in technological familiarity. AI has emerged as a promising tool to support co-creative activities, offering flexibility and creative assistance, but its role in facilitating intergenerational connection remains underexplored. In this study, we conducted a user study with 29 grandparent-grandchild groups engaged in AI-supported story creation to examine how AI-assisted co-creation can foster meaningful intergenerational bonds. Our findings show that grandchildren managed the technical aspects, while grandparents contributed creative ideas and guided the storytelling. AI played a key role in structuring the activity, facilitating brainstorming, enhancing storytelling, and balancing the contributions of both generations. The process fostered mutual appreciation, with each generation recognizing the strengths of the other, leading to an engaging and cohesive co-creation process. We offer design implications for integrating AI into intergenerational co-creative activities, emphasizing how AI can enhance connection across skill levels and technological familiarity.