New subclasses of bi-univalent functions with bounded boundary rotation are presented in this study. We acquired estimates for the initial coefficients |𝑎2| , |𝑎3| and |𝑎4| . Furthermore, we have verified the specific situations satisfying the famous hypothesis of Brannan and Clunie. Additionally, we have obtained the well-known Fekete–Szegö inequality for the newly identified bi-univalent function subclasses. Our results not only improve, but also extend several existing results as particular cases.