Information retrieval systems have traditionally relied on exact term match methods such as BM25 for first-stage retrieval. However, recent advancements in neural network-based techniques have introduced a new method called dense retrieval. This approach uses a dual-encoder to create contextual embeddings that can be indexed and clustered efficiently at run-time, resulting in improved retrieval performance in Open-domain Question Answering systems. In this paper, we apply the dense retrieval technique to conversational search by conducting experiments on the CAsT benchmark dataset. We also propose an end-to-end conversational search system called GPT2QR+DPR, which incorporates various query reformulation strategies to improve retrieval accuracy. Our findings indicate that dense retrieval outperforms BM25 even without extensive fine-tuning. Our work contributes to the growing body of research on neural-based retrieval methods in conversational search, and highlights the potential of dense retrieval in improving retrieval accuracy in conversational search systems.