We introduce an adaptive Gaussian process (AGP) as an alternative to the successive constraint method (SCM) for predicting the lower bound of a stability factor in reduced basis (RB) error analysis. This study compares AGP with the SCM using two geometrically parameterized problems: linear elastostatic and Helmholtz acoustics. The results show that AGP significantly outperforms the SCM, providing sharper and faster a posteriori error estimation of RB solutions. Although AGP fails to achieve rigorous error estimation for the Helmholtz acoustic problem with a single RB function, it attains rigorous error estimation in most cases. Overall, AGP is found to be heuristically acceptable for certified RB analysis. This research may significantly benefit the static condensation RB element (scRBE) method, which requires numerous a posteriori error estimations of reduced bubble functions for scRBE solution error estimation.