This paper tackles several challenges that arise when integrating Automatic Speech Recognition (ASR) and Machine Translation (MT) for real-time, on-device streaming speech translation. Although state-of-the-art ASR systems based on Recurrent Neural Network Transducers (RNN-T) can perform real-time transcription, achieving streaming translation in real-time remains a significant challenge. To address this issue, we propose a simultaneous translation approach that effectively balances translation quality and latency. We also investigate efficient integration of ASR and MT, leveraging linguistic cues generated by the ASR system to manage context and utilizing efficient beam-search pruning techniques such as time-out and forced finalization to maintain system's real-time factor. We apply our approach to an on-device bilingual conversational speech translation and demonstrate that our techniques outperform baselines in terms of latency and quality. Notably, our technique narrows the quality gap with non-streaming translation systems, paving the way for more accurate and efficient real-time speech translation.