Heuristics and cognitive biases are an integral part of human decision-making. Automatically detecting a particular cognitive bias could enable intelligent tools to provide better decision-support. Detecting the presence of a cognitive bias currently requires a hand-crafted experiment and human interpretation. Our research aims to explore conversational agents as an effective tool to measure various cognitive biases in different domains. Our proposed conversational agent incorporates a bias measurement mechanism that is informed by the existing experimental designs and various experimental tasks identified in the literature. Our initial experiments to measure framing and loss-aversion biases indicate that the conversational agents can be effectively used to measure the biases.