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In multi-robot system (MRS) bounding overwatch, it is crucial to determine which point to choose for overwatch at each step and whether the robots' positions are trustworthy so that the overwatch can be performed effectively. In this paper, we develop a Bayesian optimization based computational trustworthiness model (CTM) for the MRS to select overwatch points. The CTM can provide real-time trustworthiness evaluation for the MRS on the overwatch points by referring to the robots' situational awareness information, such as traversability and line of sight. The evaluation can quantify each robot's trustworthiness in protecting its robot team members during the bounding overwatch. The trustworthiness evaluation can generate a dynamic cost map for each robot in the workspace and help obtain the most trustworthy bounding overwatch path. Our proposed Bayesian based CTM and motion planning can reduce the number of explorations for the workspace in data collection and improve the CTM learning efficiency. It also enables the MRS to deal with the dynamic and uncertain environments for the multi-robot bounding overwatch task. A robot simulation is implemented in ROS Gazebo to demonstrate the effectiveness of the proposed framework.