  We calculate the amplitude of gg->bb(bar) production for the colour singlet,
J_z=0 di-gluon state at O(\alpha_S^2) order. We consider the cancellation, and
a realistic cutoff, of the infrared divergent terms. We show that the one-loop
radiative QCD contributions effectively reduce the Born level result for the
central exclusive bb(bar) cross section at the LHC. This process is essentially
the only irreducible QCD background to the exclusive H->bb(bar) signal.
