Bi-univalent functions, which are analytic and univalent in the open unit disk, have been a significant area of research in complex analysis due to their rich geometric properties. This study introduces a novel subclass of bi-univalent functions, called the Bazileviˇc functions class, which is created via the convolution of Balancing polynomials. We calculated the bounds for the Fekete-Szeg¨o inequality as well as the initial coefficients |a₂| and |a₃|. We have also included several relevant corollaries.