The rise of human-like conversational agents such as chatbots and robo-Advisors have motivated researchers to exploit the property of 'anthropomorphizing' in conversational agents who can facilitate an array of real-world applications. Since human can naturally detect respondents' emotions embedded in their responses and constantly adapt to varying conversational contexts, it is desirable to equip chatbots or robo-Advisors with the corresponding emotion-sensitive conversational generation capabilities to better mimic human-like intelligence (i.e., anthropomorphizing). However, the design and development of emotion-sensitive conversational agents are still in its infant stage. To fill the aforementioned research gap, we propose a deep learning-based emotion detection method for the development of emotion-sensitive conversational agents such as robo-Advisors in this paper. In particular, we propose a new hybrid deep learning approach which combines the merits of pre-Trained deep learning models such as BERT and Bi-LSTM by using a residual connection method which supports a layer-wise connection approach to stabilize the fine-Tuning process and bootstrap the overall emotion classification performance. Based on two well-known benchmark emotion corpora, namely IEMOCAP and FRIENDS, our rigorous experiments reveal that the proposed hybrid deep learning model with the residual connection method achieves promising emotion classification performance, which lays a solid foundation for the development of emotion-sensitive conversational agents such as chatbots and robo-Advisors.