  The in-medium masses of the bottomonium ground states [$1S$ ($\Upsilon (1S),
\eta_b$) and $1P$ ($\chi_{b0},\chi_{b1}$)] are investigated in the magnetized
vacuum (nuclear medium), using the QCD sum rule framework. In QCD sum rule
approach, the mass modifications are calculated in terms of the medium
modifications of the scalar and twist-2 gluon condensates, which are obtained
in the nuclear medium, from the medium change of a scalar dilaton field, $\chi$
within a chiral effective model. The in-medium masses of the bottomonium ground
states are observed to decrease with increasing density. P-wave states are
observed to have more appreciable mass-shifts than the S-wave states. In the
present investigation, the effects of spin-mixing between 1S bottomonium
states, $\Upsilon(1S)$ and $\eta_b$ are taking into account in presence of an
external magnetic field. The contribution of magnetic fields are seen to be
dominant via spin-magnetic field interaction effects, which leads to an
appreciable rise and drop in the in-medium masses of the longitudinal component
of vector $1S$ state ($\Upsilon$) and pseudoscalar state ($\eta_b$)
respectively. For zero magnetic field, the effects of baryon density on the
bottomonium ground states in isospin asymmetric nuclear medium are observed to
be quite appreciable. These should have observable consequences for the
production of the open and hidden bottom meson states resulting from high
energy asymmetric nuclear collisions in facilities which probe high density
baryonic matter. There is observed to be large contributions to the masses of
the longitudinal component of the vector bottomonium state, $\Upsilon (1S)$ and
pesudoscalar state $\eta_b$ in strong magnetic fields.
