This paper studies how to enhance the document representation for the bi-encoder approach in dense document retrieval. The bi-encoder, separately encoding a query and a document as a single vector, is favored for high efficiency in large-scale information retrieval, compared to more effective but complex architectures. To combine the strength of the two, the multi-vector representation of documents for bi-encoder, such as ColBERT preserving all token embeddings, has been widely adopted. Our contribution is to reduce the size of the multi-vector representation, without compromising the effectiveness, supervised by query logs. Our proposed solution decreases the latency and the memory footprint, up to 8- and 3-fold, validated on MSMARCO and real-world search query logs.