Using the Bethe ansatz we study the spectrum of boundary bound states of the SU(N) generalization of the one-dimensional Hubbard model with open boundaries and applied boundary potentials. The number of electrons bound by the boundary field is found from the surface contribution to the energy. Finite size corrections to the low-lying energies in this system and use of the predictions of boundary conformal field theory allows us to study the exponents related to the orthogonality catastrophe and absorption edges.