We report a comprehensive study of the ground-state properties of one and two bosonic impurities immersed in small one-dimensional optical lattices loaded with a few interacting bosons. We model the system with a two-component Bose-Hubbard model and solve the problem numerically by means of the exact diagonalization method. We report polaron and bipolaron energies across the superfluid to Mott-insulator transition and confirm the formation of bipolaron bound states induced by repulsive interactions. In particular, we found that an insulator bath induces tightly bound bipolarons, whereas a superfluid bath induces shallower bound states.