Drones pose privacy concerns such as surveillance and stalking. Many technology-based or policy-based mechanisms have been proposed to mitigate these concerns. However, it is unclear how drone controllers and bystanders perceive these mechanisms and whether people intend to adopt them. In this paper, we report results from two rounds of online survey with 169 drone controllers and 717 bystanders in the U.S. We identified respondents' perceived pros and cons of eight privacy mechanisms. We found that owner registration and automatic face blurring individually received most support from both controllers and bystanders. Our respondents also suggested using varied combinations of mechanisms under different drone usage scenarios, highlighting their context-dependent preferences. We outline a set of important questions for future privacy designs and public policies of drones. Copyright is held by the owner/author(s). Publication rights licensed to ACM.