We search for bottomonium states in gamma(2S) -> (b (b) over bar)gamma decays with an integrated luminosity of 24.7 fb(-1) recorded at the gamma(2S) resonance with the Belle detector at KEK, containing (157.8 +/- 3.6) x 10(6) gamma(2S) events. The (b (b) over bar) system is reconstructed in 26 exclusive hadronic final states composed of charged pions, kaons, protons, and K-0(S) mesons. We find no evidence for the state recently observed around 9975 MeV (X-b (b) over bar) in an analysis based on a data sample of 9.3 x 10(6) gamma(2S) events collected with the CLEO III detector. We set a 90% confidence level upper limit on the branching fraction B[gamma(2S) -> X-b (b) over bar gamma] x Sigma(i) B[X-b (b) over bar -> h(i)] < 4.9 x 10(-6), summed over the exclusive hadronic final states employed in our analysis. This result is an order of magnitude smaller than the measurement reported with CLEO data. We also set an upper limit for the eta(b)(1S) state of B[gamma(2S) -> eta(b)(1S)gamma] x Sigma B-i[eta(b)(1S) -> h(i)] < 3.7 x 10(-6).