We study the problem of constructing confidence intervals for the optimal value of a stochastic programming problem by using bootstrapping. Bootstrapping is a resampling method used in the statistical inference of unknown parameters for which only a small number of samples can be obtained. One such parameter is the optimal value of a stochastic optimization problem involving complex spatio-temporal uncertainty, for example coming from weather prediction. However, bootstrapping works provably better than traditional inference technique based on the central limit theorem only for parameters that are finite-dimensional and smooth functions of the moments, whereas the optimal value of the stochastic optimization problem is not. In this paper we propose and analyze a new bootstrap-based estimator for the optimal value that gives higher-order confidence intervals.