The paper studies the excitation of the Th229 nucleus to the anomalously low-lying isomeric state 3/2+(8.28±0.17 eV) in the electron bridge process via the continuum of the electron spectrum. Resonant excitation of the nucleus was found to be always possible in the scheme, no matter where the electron levels of an atom or ion were located. Formulas for the excitation cross section by narrow and wide laser lines are obtained. In the resonance, where the process under consideration turns into laser photoionization followed by nuclear excitation in electron capture, the cross section of the process was shown to be comparable in magnitude with that of the photoionization of the thorium atom. Experimental schemes for testing the effect were proposed, which would allow measuring the frequency of the nuclear isomeric transition 3/2+→5/2+ to a high precision, which is the first-priority (and still unresolved) task for creating a nuclear clock.