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We study the problem faced by a bike-sharing service provider who needs to manage a fleet of bikes over a set of bike-stations, each with given capacity and time-varying stochastic demand. In particular, we focus on One-way bike sharing systems with transshipment in which: (1) The user can pick up a bike at a station and drop it off at a different station; (2) Transshipment of bikes among stations is performed at the end of the day, to have the optimal number of bikes at each station at the beginning of the service on the next day. For this problem, we propose two-stage and multistage stochastic optimization models, to determine the optimal number of bikes to assign to each station at the beginning of the service. Numerical results are provided for the bike-sharing service “LaBiGi” in Bergamo (Italy), from which managerial insights are drawn.