As social robots become increasingly prevalent in day-to-day environments, they will participate in conversations and appropriately manage the information shared with them. However, little is known about how robots might appropriately discern the sensitivity of information, which has major implications for human-robot trust. As a first step to address a part of this issue, we designed a privacy controller, Confidant, for conversational social robots, capable of using contextual metadata (e.g., sentiment, relationships, topic) from conversations to model privacy boundaries. Afterwards, we conducted two crowdsourced user studies. The first study (n=174) focused on whether a variety of human-human interaction scenarios were perceived as either private/sensitive or non-private/non-sensitive. The findings from our first study were used to generate association rules. Our second study (n=95) evaluated the effectiveness and accuracy of the privacy controller in human-robot interaction scenarios by comparing a robot that used our privacy controller against a baseline robot with no privacy controls. Our results demonstrate that the robot with the privacy controller outperforms the robot without the privacy controller in privacy-awareness, trustworthiness, and social-awareness. We conclude that the integration of privacy controllers in authentic human-robot conversations can allow for more trustworthy robots. This initial privacy controller will serve as a foundation for more complex solutions.