In this article, we define new families of normalized holormorphic and bi-univalent functions $\mathcal{R}_{\Sigma}(µ,\gamma,\lambda;\vartheta)$ and $\mathcal{F}_{\Sigma}(µ,\gamma,\lambda;\vartheta)$ which involve the Bazilevič functions and the $\lambda$-pseudo functions defined in the unit disk $U$. We determine the coefficient estimates for the initial Taylor-Maclaurin coefficients $|a_2|$ and $|a_3|$ and resolve the Fekete-Szegö type inequalities for these families. In addition, we point out several special cases and consequences of our results.