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As new grid edge technologies emerge—such as rooftop solar panels, battery storage, and controllable water heaters—quantifying the uncertainties of building load forecasts is becoming more critical. The recent adoption of smart meter infrastructures provided new granular data streams, largely unavailable just ten years ago, that can be utilized to better forecast building-level demand. This paper uses Bayesian Structural Time Series for probabilistic load forecasting at the residential building level to capture uncertainties in forecasting. We use sub-hourly electrical submeter data from 120 residential apartments in Singapore that were part of a behavioral intervention study. The proposed model addresses several fundamental limitations through its flexibility to handle univariate and multivariate scenarios, perform feature selection, and include either static or dynamic effects, as well as its inherent applicability for measurement and verification. We highlight the benefits of this process in three main application areas: (1) Probabilistic Load Forecasting for Apartment-Level Hourly Loads; (2) Submeter Load Forecasting and Segmentation; (3) Measurement and Verification for Behavioral Demand Response. Results show the model achieves a similar performance to ARIMA, another popular time series model, when predicting individual apartment loads, and superior performance when predicting aggregate loads. Furthermore, we show that the model robustly captures uncertainties in the forecasts while providing interpretable results, indicating the importance of, for example, temperature data in its predictions. Finally, our estimates for a behavioral demand response program indicate that it achieved energy savings; however, the confidence interval provided by the probabilistic model is wide. Overall, this probabilistic forecasting model accurately measures uncertainties in forecasts and provides interpretable results that can support building managers and policymakers with the goal of reducing energy use.