Aim: Accurate characterization of abdominal aortic aneurysm (AAA) and intraluminal thrombus (ILT) materials is key to improving rupture risk assessment. This study presents a patient-specific framework that couples finite element (FE) modeling and Bayesian optimization to estimate tissue material properties. Methods: Four patients' 3D cine-magnetic resonance imaging (MRI) scans were segmented to reconstruct the aortic wall displacements throughout the cardiac cycle, focusing on the AAA region and including the ILT. Quadratic tetrahedral meshes were generated for FE simulations. The aortic wall tissue was modeled using the Gasser formulation to account for fiber orientation and anisotropy, resulting in five material parameters, while the ILT was treated as an isotropic, nearly incompressible material using a neo-Hookean material model, with one material coefficient. For each patient, 200 FE simulations of systolic pressure application to the recovered zero-pressure configuration were run, varying 200 material parameters combinations. To infer optimal parameters, a Gaussian process surrogate model was constructed. Bayesian optimization was then applied, iteratively balancing exploration and exploitation through an expected improvement acquisition function, in order to minimize the root mean squared error (RMSE) between computationally simulated and MRI-derived displacements between systolic and diastolic phases. Results: The resulting patient-specific computational models accurately reproduced the image-derived deformations (RMSE<10% in all patients). High stress concentrations were found in bulging regions and curvature peaks, such as proximal and distal AAA necks, while areas beneath the ILT showed reduced stresses, consistent with its hypothesized mechanical buffering effect. Conclusions: This approach enables data-driven calibration of AAA and ILT material properties using imaging alone and offers a powerful tool for patient-specific rupture risk prediction and clinical decision support.