Geomagnetic storms, which are governed by the plasma magnetohydrodynamics of the solar-interplanetary-magnetosphere system, entail a formidable challenge for physical forward modeling. Yet, the abundance of high quality observational data has been amenable for the application of data-hungry neural networks to geomagnetic storm forecasting. Previous applications of neural networks to storm forecasting have utilized solar wind observations from the Earth-Sun first Lagrangian point (L1) or closer and have all generated deterministic output without uncertainty estimates. Furthermore, forecasting work has focused on indices that are also sensitive to induced internal magnetic fields, complicating the forecasting problem with another layer of non-linearity. We address these points, presenting neural networks trained on observations from both the solar disk and the L1 point. Our architecture generates reliable probabilistic forecasts over Est, the external component of the disturbance storm time index, showing that neural networks can gauge confidence in their output.