Dockless sharing bikes play an increasingly significant role in transit transfer, especially for the first/last mile. However, it is not always accessible for users to find sharing bicycles. The objective of this paper is to assess the accessibility of dockless sharing bikes from a network perspective, which would provide a decision-making basis not only for potential bike users but also for urban planners, policymakers, and bicycle suppliers to optimize sharing-bike systems. Considering bicycle travel characteristics, a hierarchical clustering algorithm was applied to construct the dockless sharing-bike network. The social network analysis (SNA) method was adopted to assess the accessibility of the bike network. Then, a spatial interaction model was chosen to conduct a correlation analysis to compare the accessibility obtained from the SNA approach. The case study of Shanghai indicates a strong connection between the accessibility and the SNA indicators with the correlation coefficient of 0.779, which demonstrates the feasibility of the proposed method. This paper contributes to a deep understanding of dockless sharing-bike network accessibility since the SNA approach considers both the interaction barriers and the network structure of a bicycle network. The developed methodology requires fewer data and is easy to operate. Thus, it can serve as a tool to facilitate the smart management of sharing bikes for improving a sustainable transportation system.