When we use simulation to estimate the performance of a stochastic system, lack of fidelity in the random input models can lead to poor system performance estimates. Since the components of many complex systems could be dependent, we want to build input models that faithfully capture such key properties. In this paper, we use the flexible NORmal To Anything (NORTA) representation for dependent inputs. However, to use the NORTA representation we need to estimate the marginal distribution parameters and a correlation matrix from real-world data, introducing input uncertainty. To quantify this uncertainty, we employ the bootstrap to capture the parameter estimation error and an equation-based stochastic kriging metamodel to propagate the input uncertainty to the output mean. Asymptotic analysis provides theoretical support for our approach, while an empirical study demonstrates that it has good finite-sample performance.