The effect of Bi incorporation on the conduction band structure of Ga(AsBi) alloys is revealed by a direct estimation of the electron effective mass via cyclotron resonance absorption spectroscopy at THz frequencies in pulsed magnetic fields up to 65 T. A strong enhancement in the electron effective mass with increasing Bi content is reported, with a value of mass $\ensuremath{\sim}40%$ higher than that in GaAs for $\ensuremath{\sim}1.7%$ of Bi. This experimental evidence unambiguously indicates a Bi-induced perturbation of the host conduction band states and calls for a deep revision of the theoretical models describing dilute bismides currently proposed in the literature, the majority of which neglect or exclude that the incorporation of a small percentage of Bi may affect the conduction band states of the host material.