The sustainable use of recycled aggregate concrete (RAC) is a critical pathway toward resource-efficient and environmentally responsible construction. However, the mechanical performance of RAC—particularly its elastic modulus—exhibits pronounced variability due to the heterogeneous quality and microstructural defects of recycled aggregates. This variability complicates the establishment of reliable predictive models and equations for elastic modulus estimation and restricts RAC’s broader structural implementation. Conventional empirical and machine-learning-based models (e.g., support vector machine, random forest, and artificial neural networks) are typically dataset-specific, prone to overfitting, and incapable of quantifying bias and uncertainty, making them unsuitable for heterogeneous materials data. This study introduces a bias-aware and more accurate predictive framework that integrates the Tabular Prior-data Fitted Network (TabPFN) with Monte Carlo Bias Estimation (MCBE)—for the first time applied in RAC materials research. A database containing 1161 RAC samples from diverse literature sources was established. This database includes key parameters such as apparent density ranging from 2270 kg/m³ to 3150 kg/m³, water absorption from 0.75% to 7.81%, replacement ratio from 0% to 100%, and compressive strength values ranging from 10.00 MPa to 108.51 MPa. MCBE quantified representational bias and guided targeted data augmentation, while TabPFN—pretrained on millions of Bayesian inference tasks—achieved R² = 0.912 and RMSE = 1.65 GPa without any hyperparameter tuning. Feature attribution analysis confirmed compressive strength as the most influential factor governing the elastic modulus, consistent with established composite mechanics principles. The proposed TabPFN–MCBE framework provides a reliable, bias-corrected, and transferable approach for modeling recycled aggregate concrete (RAC). It enables accurate predictions that are both trustworthy and interpretable, advancing the use of data-driven methods in sustainable materials design.