In this paper, we obtain explicit upper bounds for the initial seven coefficients and their inverses for a subclass of bi-univalent functions defined via subordination. Using coefficient estimates associated with the Carathodory class and coefficient comparison techniques, expressions for the bounds of a2, a3, , a7 are derived. Moreover, it is proved that the first seven inverse coefficients admit the same upper bounds as the corresponding coefficients of the original function. These findings generalize several existing results concerning lower-order coefficients and provide a framework for further investigations of higher-order coefficient and Hankel determinant problems in the theory of bi-univalent functions.