To properly evaluate the ability of robots to operate autonomously in the real world, it is necessary to develop methods for quantifying their self-righting capabilities. Here, we improve upon a sampling-based framework for evaluating self-righting capabilities that was previously validated in two dimensions. To apply this framework to realistic robots in three dimensions, we require algorithms capable of scaling to high-dimensional configuration spaces. Therefore, we introduce a novel adaptive sampling approach that biases queries toward the transitional states of the system, thus, identifying the critical transitions of the system using substantially fewer samples. To demonstrate this improvement, we compare our approach to results that were generated via the previous framework and were validated on hardware platforms. Finally, we apply our technique to a high-fidelity three-dimensional model of a US Navy bomb-defusing robot, which was too complex for the previous framework to analyze.