Conversational agents are being used to help in the screening, assessment, diagnosis, and treatment of common mental health disorders. In this paper, we propose a bootstrapping approach for the development of a digital mental health conversational agent (i.e., chatbot). We start from a basic rule-based expert system and iteratively move towards a more sophisticated platform composed of specialized chatbots each aiming to assess and pre-diagnose a specific mental health disorder using machine learning and natural language processing techniques. During each iteration, user feedback from psychiatrists and patients are incorporated into the iterative design process. A survival of the fittest approach is also used to assess the continuation or removal of a specialized mental health chatbot in each generational design. We anticipate that our unique and novel approach can be used for the development of conversational mental health agents with the ultimate goal of designing a smart chatbot that delivers evidence-based care and contributes to scaling up services while decreasing the pressure on mental health care providers.