The realization of a Chinese-English bilingual speech dialogue system through machine translation technology involves developing a sophisticated system capable of seamlessly translating spoken language between Chinese and English in real-time. This system employs cutting-edge machine learning algorithms, neural networks, and natural language processing techniques to accurately interpret and translate speech inputs from one language to another. By integrating advanced speech recognition and translation models, users can engage in fluid and natural conversations across language barriers, opening up new possibilities for cross-cultural communication and interaction. This paper introduces a Statistical Phase-based Bilingual Speech (SPBS) system designed to facilitate seamless language translation and dialogue between multiple languages, with a focus on Chinese and English. Leveraging advanced machine learning models and techniques, such as Recurrent Neural Networks (RNN) with Bidirectional Long Short-Term Memory (Bi-LSTM) architecture, the SPBS system achieves high translation accuracy, computational efficiency, and fluency of translations. The system's multilingual model attains an impressive translation accuracy of 97% while processing 10 sentences per second, with positive feedback on the fluency of translations. Trained on a substantial dataset of 1 million bilingual sentence pairs, the SPBS model maintains a compact size of 500 MB. Furthermore, the paper presents the machine learning settings and training progress of the SPBS system, demonstrating its effectiveness in accurately classifying and translating speech inputs across languages. The system's multilingual model attains an impressive translation accuracy of 97% while processing 10 sentences per second, with positive feedback on the fluency of translations. Trained on a substantial dataset of 1 million bilingual sentence pairs, the SPBS model maintains a compact size of 500 MB.