We present a novel approach to mitigate bias in facial expression recognition (FER) models. Our method aims to reduce sensitive attribute information such as gender, age, or race, in the embeddings produced by FER models. We employ a kernel mean shrinkage estimator to estimate the kernel mean of the distributions of the embeddings associated with different sensitive attribute groups, such as young and old, in the Hilbert space. Using this estimation, we calculate the maximum mean discrepancy (MMD) distance between the distributions and incorporate it in the classifier loss along with an adversarial loss, which is then minimized through the learning process to improve the distribution alignment. Our method makes sensitive attributes less recognizable for the model, which in turn promotes fairness. Additionally, for the first time, we analyze the notion of attractiveness as an important sensitive attribute in FER models and demonstrate that FER models can indeed exhibit biases towards more attractive faces. To prove the efficacy of our model in reducing bias regarding different sensitive attributes (including the newly proposed attractiveness attribute), we perform several experiments on two widely used datasets, CelebA and RAF-DB. The results in terms of both accuracy and fairness measures outperform the state-of-the-art in most cases, demonstrating the effectiveness of the proposed method.