This study introduces a novel computational approach for testing conditional independence (BB CI test) within causal Directed Acyclic Graphs (DAGs), leveraging Bayesian non-parametric bootstrap and machine learning techniques. Our method offers an alternative for validating the assumptions underpinning causal DAGs. Through simulation studies and an industrial case analysis, we demonstrate the test procedure in accurately assessing conditional independence, comparing it with the Generalized Covariance Measure (GCM) test. Our findings suggest that the BB CI test is advantageous in scenarios where existing methods may falter due to violations of model assumptions. This research contributes to the causal inference literature by providing a computational tool for researchers and practitioners to validate causal models.