Autonomous motion planning is critical for efficient and safe underwater manipulation in dynamic marine environments. Current motion planning methods often fail to effectively utilize prior motion experiences and adapt to real-time uncertainties inherent in underwater settings. In this paper, we introduce an Adaptive Heuristic Motion Planner framework that integrates a Heuristic Motion Space (HMS) with Bayesian Networks to enhance motion planning for autonomous underwater manipulation. Our approach employs the Probabilistic Roadmap (PRM) algorithm within HMS to optimize paths by minimizing a composite cost function that accounts for distance, uncertainty, energy consumption, and execution time. By leveraging HMS, our framework significantly reduces the search space, thereby boosting computational performance and enabling real-time planning capabilities. Bayesian Networks are utilized to dynamically update uncertainty estimates based on real-time sensor data and environmental conditions, thereby refining the joint probability of path success. Through extensive simulations and real-world test scenarios, we showcase the advantages of our method in terms of enhanced performance and robustness. This probabilistic approach significantly advances the capability of autonomous underwater robots, ensuring optimized motion planning in the face of dynamic marine challenges.