In bike sharing systems (BSSs), the uncoordinated movements of customers using bikes lead to empty or congested stations, which causes a significant loss in customer demand. In order to reduce the lost demand, a wide variety of existing research has employed a fixed set of historical demand patterns to design efficient bike repositioning solutions. However, the progress remains slow in understanding the underlying uncertainties in demand and designing proactive robust bike repositioning solutions. To bridge this gap, we propose a dynamic bike repositioning approach based on a probabilistic satisficing method which uses the uncertain demand parameters that are learnt from historical data. We develop a novel and computationally efficient mixed integer linear program for maximizing the probability of satisfying the uncertain demand so as to improve the overall customer satisfaction and efficiency of the system. Extensive experimental results from a simulation model built on a real-world bike sharing data set demonstrate that our approach is not only robust to uncertainties in customer demand, but also outperforms the existing state-of-the-art repositioning approaches in terms of reducing the expected lost demand.