This study presents a data-driven regression framework for predicting front-side and rear-side plane-of-array (PoA) irradiance in a bifacial photovoltaic (PV) system using synchronized field measurements. The proposed approach is developed and validated using real-world data obtained from NREL’s vertical bifacial PV testbed and relies exclusively on routinely measured meteorological, surface-related, and temporal variables, including global and diffuse horizontal irradiance, ambient temperature, wind speed, ground albedo, a reflective ground indicator, and cyclic time-of-day features. Six supervised machine learning models with varying complexity Linear Regression, K-Nearest Neighbors, Support Vector Regression, Random Forest, Extreme Gradient Boosting, and Multilayer Perceptron are systematically evaluated to assess their ability to predict Front_PoA and Rear_PoA under identical input conditions. Model performance is quantified using RMSE, MAE, and correlation metrics, revealing clear advantages of nonlinear and ensemble-based models over linear formulations. Random Forest achieves the best overall predictive accuracy for both irradiance components (Front_PoA: RMSE = 0.188, MAE = 0.061, r = 0.982; Rear_PoA: RMSE = 0.236, MAE = 0.080, r = 0.973), while rear-side predictions consistently exhibit higher uncertainty, reflecting the more complex radiative environment of the rear surface. To enhance physical interpretability, SHAP-based analyses are employed to quantify the contribution of each input variable and to examine nonlinear response patterns and interaction effects. The results indicate that front-side irradiance is primarily governed by global irradiance and diurnal solar geometry, whereas rear-side irradiance is strongly influenced by surface-related factors such as ground albedo and the presence of reflective ground cover, confirming the conditional and interaction-driven nature of rear-side irradiance formation in bifacial systems. Overall, this study demonstrates that accurate and interpretable prediction of both front and rear PoA irradiance can be achieved using a compact set of easily measurable inputs.