The in-medium partial decay widths of $Upsilon (4S) rightarrow Bbar B$ in magnetized asymmetric nuclear matter are studied using a field theoretic model for composite hadrons with quark/antiquark constituents. The medium modifications of the decay widths of $Upsilon (4S)$ to $Bbar B$ pair in magnetized matter, arise due to the mass modifications of the decaying $Upsilon (4S)$ as well as of the produced $B$ and $bar B$ mesons. The effects of the anomalous magnetic moments for the proton and neutron are taken into consideration in the present investigation. The presence of the external magnetic field is observed to lead to different mass modifications within the $B (B^+, B^0)$ as well as the $bar B (B^-, bar {B^0})$ doublets, even in isospin symmetric nuclear matter, due to the difference in the interactions of the proton and the neutron to the electromagnetic field. This leads to difference in the upsilon decay widths to the neutral ($B^0 bar {B^0}$) and the charged ($B^+ B^-$) pairs in the magnetized symmetric nuclear matter. The isospin asymmetry is observed to lead to quite different behaviours for the $Upsilon (4S)$ decay widths to the charged and neutral $Bbar B$. In the presence of the magnetic field, the Landau level contributions give rise to positive shifts in the masses of the charged $B$ and $bar B$ mesons. This leads to the decay of $Upsilon(4S)$ to the charged $B^+ B^-$ to be suppressed as compared to the neutral $Bbar B$ pair, especially at low densities. This may lead to suppression in the production of the charged $B^pm$ mesons as compared to the neutral $B^0$ and $bar {B^0}$ mesons at LHC and RHIC.
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