  We continue the study of Specht modules labelled by hook bipartitions for the
Iwahori--Hecke algebra of type $B$ with $e\in\{3,4,\dots\}$ via the cyclotomic
Khovanov--Lauda--Rouquier algebra $\mathscr{H}_n^{\Lambda}$. Over an arbitrary
field, we explicitly determine the graded decomposition submatrices for
$\mathscr{H}_n^{\Lambda}$ comprising rows corresponding to hook bipartitions.
