  We consider b-jet hadroproduction in the quasi-multi-Regge-kinematics
approach based on the hypothesis of gluon and quark Reggeization in t-channel
exchanges at high energies. The preliminary data on inclusive b-jet and b
anti-b-dijet production taken by the CDF Collaboration at the Fermilab Tevatron
are well described without adjusting parameters. We find the main contribution
to inclusive b-jet production to be the scattering of a Reggeized gluon and a
Reggeized b-quark to a b quark, which is described by the effective
Reggeon-Reggeon-quark vertex. The main contribution to b anti-b-pair production
arises from the scattering of two Reggeized gluons to a b anti-b pair, which is
described by the effective Reggeon-Reggeon-quark-quark vertex. Our anaysis is
based on the Kimber-Martin-Ryskin prescription for unintegrated gluon and quark
distribution functions using as input the Martin-Roberts-Stirling-Thorne
collinear parton distribution functions of the proton.
