Accurate modeling of atomic masses with reliable uncertainty quantification is essential for understanding heavy-element production in astrophysical environments. This remains challenging because uncertainties arise not only from model parameters but also from structural limitations, often leading to underestimation when extrapolating beyond known nuclei. Here, we introduce SPICE, a probabilistic nuclear mass model that uses local Bayesian averaging to emulate mixing between low-lying nuclear configurations within a shell-model-inspired framework. By incorporating configurations associated with excitations across harmonic-oscillator and spin-orbit major shells, the model achieves root-mean-square deviations of about 500 keV with only 10-13 parameters. Our results show that local configuration mixing improves predictive accuracy and provides insight into evolving shell structure in neutron- and proton-rich regions, with potential extensions to include configuration mixing effects from non-orthogonal configurations.