Multimodal Aspect-Based Sentiment Analysis (MABSA) has emerged as a crucial task for fine-grained opinion mining, leveraging both textual and visual information to infer sentiment polarity toward specific aspects. While current methods focus primarily on cross-modal feature fusion, they often fail to address the critical challenge of spurious correlations - statistically prevalent but causally unreliable associations between multimodal features and sentiment labels. This paper proposes BU-MABSA, a novel bias-unlearning framework grounded in causal inference theory, to systematically identify and mitigate such spurious correlations. At the core of our approach lies a structured causal model that decomposes multimodal influences into direct pathways (which may contain biases) and indirect cross-modal pathways (which capture more reliable interactions). We develop a hybrid intervention strategy that combines do-calculus operations with counterfactual reasoning to isolate and suppress modality-specific biases during model training. Furthermore, the framework incorporates a confidence calibration mechanism that dynamically adjusts prediction reliability based on estimated bias effects. Extensive experiments demonstrate that BU-MABSA achieves state-of-the-art performance, with absolute improvements in accuracy and F1-score over existing methods. The framework also shows enhanced robustness by significantly reducing overconfidence errors while maintaining strong generalization capability across different data distributions.