The properties of semiconductors can be crucially impacted by midgap states induced by dopants, which can be native or intentionally incorporated in the crystal lattice. For Bernal-stacked bilayer graphene (BLG), which has a tunable band gap, the existence of midgap states induced by dopants or adatoms has been investigated theoretically and observed indirectly in electron transport experiments. Here, we characterize BLG midgap states in real space, with atomic-scale resolution with scanning tunneling microscopy and spectroscopy. We show that the midgap states in BLG-for which we demonstrate gate tunability-appear when the dopant is hosted on the nondimer sublattice sites. We further evidence the presence of narrow resonances at the onset of the high-energy bands (valence or conduction, depending on the dopant type) when the dopants lie on the dimer sublattice sites. Our results are supported by tight-binding calculations that agree remarkably well with the experimental findings.