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Urban stormwater management is shifting its attention from traditional centralized engineering solutions to a distributed and greener approach, namely Green Infrastructure (GI). However, uncertainties concerning GI's efficacy for reducing runoff and pollutants are a barrier to the adoption of GI. One strategy to deal with the uncertainty is to implement GI adaptively, in which stormwater managers can learn and adjust their plans over time to avoid undesired outcomes. We propose a new class of GI planning methods based on two-stage stochastic programming and Bayesian learning, which accounts for projected information gains and decision makers' objectives and willingness to accept risk. In the hypothetical example, the model identifies four categories of investment strategies and quantifies their benefits and costs: all-in, greedy investment plus deferral, mixed investments plus deferral, and learn-and-adjust. Which strategy is optimal depends on the user's risk attitudes, and the alternatives' costs and risks.