Recently, firms have experienced severe disasters that caused major supply disruptions. In this paper we study the strategies of dual sourcing and inventory management of a manufacturer facing disrupted supplies. Although abundant research has been conducted in this field, researchers rarely address the problem in the presence of information asymmetry or imperfection, which occurs because unstable supplies are often highly volatile and unpredictable in early stages. Without accurate and prompt forecasts of upstream supplies, it is difficult for a manufacturer to manage the disruption risks in an optimal manner. Here, a Bayesian model is proposed to dynamically update the knowledge of supply risks, which uses Dirichlet prior distributions to achieve mathematical tractability in Bayesian updating. Optimal-sourcing strategies are studied under this framework. Simulation results show that the proposed approach is effective in cost reduction and robust in reacting to imperfect or incomplete initial knowledge of disruptions.