  We study inclusive $b$-jet and $b\bar b$-dijet production at the CERN LHC
invoking the hypothesis of gluon Reggeization in $t$-channel exchanges at high
energy. The $b$-jet cross section includes contributions from open $b$-quark
production and from $b$-quark production via gluon-to-bottom-pair
fragmentation. The transverse-momentum distributions of inclusive $b$-jet
production measured with the ATLAS detector at the CERN LHC in different
rapidity ranges are calculated both within multi-Regge kinematics and
quasi-multi-Regge kinematics. The $b\bar b$-dijet cross-section is calculated
within quasi-multi-Regge kinematics as a function of the dijet invariant mass
$M_{jj}$, the azimuthal angle between the two jets $\Delta\phi$ and the angular
variable $\chi$. At the numerical calculation, we adopt the
Kimber-Martin-Ryskin and Bl\"umlein prescriptions to derive unintegrated gluon
distribution function of the proton from its collinear counterpart, for which
we use the Martin-Roberts-Stirling-Thorne set. We find good agreement with
measurements by the ATLAS and CMS Collaborations at the LHC at the hadronic
c.m.\ energy of $\sqrt S=7$ TeV.
