Bike-sharing systems (BSS) have widely spread over many cities in the world as an environmentally friendly means to reduce air pollution and traffic congestion. This paper focuses on the bike-sharing rebalancing problem (BRP), which consists of two aspects: determining desired demands at each station and designing routes to redistribute bikes among stations. For the first task, we firstly apply the random forest, a very efficient machine learning algorithm, to forecast desired demands for each station, which can be easily implemented with distributed computing. For the second task, it belongs to the broad class of the vehicle routing problem with pickup and delivery (VRPPD). In most existing settings, all of the demands being strictly satisfied can lead to longer routes and add operational costs. In this paper, we propose a new model with unserved demands by relaxing demands satisfying constraints. Then, we design a distributed ant colony optimization (ACO) based algorithm with some specific modifications to increase its efficiency for the proposed model. We propose to use the percentage of average cost saving per bike as a metric to evaluate the performance of our method on cost-reducing and compare with existing methods and best-known values. Computational results on benchmarks show the advantage of our approach. Finally, we provide a real case study of BSS in Hangzhou, China, with insightful elaborations.