Higgs boson production in association with a high pT photon at the CERN Large Hadron Collider is analyzed, in the framework of the MSSM model, for the heavier neutral Higgs bosons. The request of an additional photon in the exclusive Higgs boson final state selects b-quark pairs among the possible initial partonic states, since gluon-gluon initial states are not allowed by C-parity conservation. Hence, the measurement of cross sections for neutral Higgs boson plus photon production can provide a clean probe of the b-quark density in the proton as well as of the b-quark Yukawa coupling. The suppression of the production rates by the b-quark electromagnetic coupling can be compensated by the enhanced Higgs boson Yukawa coupling to b's in the large tan(beta) regime. The Higgs boson decay into a tau-lepton pair is considered, and irreducible backgrounds with corresponding signal significances are evaluated.