We present a computationally efficient method to obtain the spectral function of bulk systems in the framework of steady-state density functional theory (i-DFT) using an idealized scanning tunneling microscope (STM) setup. We calculate the current through the STM tip and then extract the spectral function from the finite-bias differential conductance. The fictitious noninteracting system of i-DFT features an exchange-correlation (XC) contribution to the bias which guarantees the same current as in the true interacting system. Exact properties of the XC bias are established using Fermi-liquid theory and subsequently implemented to construct approximations for the Hubbard model. We show for two different lattice structures that the Mott metal-insulator transition is captured by i-DFT.