This paper investigates how people with blindness and low vision (BLV) use generative AI (GenAI) tools to interpret and manage visual content in their everyday lives through an interview study of 21 participants. The results show that users consider privacy risks when using GenAI in six key scenarios: self-expression, indoor/outdoor spatial privacy, social sharing, and expert content processing. In addition, users indicated design preferences for on-device processing, zero-retention guarantees, sensitive content removal, privacy-aware visual indicators, and multimodal tactile mirroring interaction methods. Based on this, we present actionable design recommendations to support user-centered visual privacy with GenAI.