Atomistic simulations can complement the scarce experimental data on free energies of molecules at bio-inorganic interfaces. In molecular simulations, adsorption free energy landscapes are efficiently explored with advanced sampling methods, but classical dynamics is unable to capture charge transfer and polarization at the solid-liquid interface. Ab initio simulations do not suffer from this flaw, but only at the expense of an overwhelming computational cost. Here, we introduce a protocol for adsorption free energy calculations that improves sampling on the timescales relevant to ab initio simulations. As a case study, we calculate adsorption free energies of the charged amino acids Lysine and Aspartate on the fully hydrated anatase (101) TiO2 surface using tight-binding forces. We find that the first-principle description of the system significantly contributes to the adsorption free energies, which is overlooked by calculations with previous methods.