We present a novel emulation scheme for ab initio many-body nuclear calculations that integrates a hierarchical framework with a Bayesian neural network. This approach enables accurate and simultaneous predictions of nuclear properties across entire isotopic chains and is broadly applicable to different regions of the nuclear chart. We benchmark our developments using the oxygen isotopic chain, achieving accurate results for ground-state energies and nuclear charge radii, while providing robust uncertainty quantification. Our framework enables global sensitivity analysis of nuclear binding energies and charge radii with respect to the low-energy constants that describe the nuclear force.