Conversational AI systems are being used in personal devices, providing users with highly personalized content. Personalized knowledge graphs (PKGs) are one of the recently proposed methods to store users' information in a structured form and tailor answers to their liking. Personalization, however, is prone to amplifying bias and contributing to the echo-chamber phenomenon. In this paper, we discuss different types of biases in conversational search systems, with the emphasis on the biases that are related to PKGs. We review existing definitions of bias in the literature: people bias, algorithm bias, and a combination of the two, and further propose different strategies for tackling these biases for conversational search systems. Finally, we discuss methods for measuring bias and evaluating user satisfaction.