In this demo we present a web-based application for selecting an effective pre-trained dense retriever to use on a private collection. Our system, DenseQuest, provides unsupervised selection and ranking capabilities to predict the best dense retriever among a pool of available dense retrievers, tailored to an uploaded target collection. DenseQuest implements a number of existing approaches, including a recent, highly effective method powered by Large Language Models (LLMs), which requires neither queries nor relevance judgments. The system is designed to be intuitive and easy to use for those information retrieval engineers and researchers who need to identify a general-purpose dense retrieval model to encode or search a new private target collection. Our demonstration illustrates conceptual architecture and the different use case scenarios of the system implemented on the cloud, enabling universal access and use. DenseQuest is available at https://densequest.ielab.io.