  We determine the essential dimension of an arbitrary semisimple group of type
$B$ of the form \[G=\big(\operatorname{\mathbf{Spin}}(2n_{1}+1)\times\cdots
\times \operatorname{\mathbf{Spin}}(2n_{m}+1)\big)/\boldsymbol{\mu}\] over a
field of characteristic $0$, for all $n_{1},\ldots, n_{m}\geq 7$, and a central
subgroup $\boldsymbol{\mu}$ of
$\operatorname{\mathbf{Spin}}(2n_{1}+1)\times\cdots \times
\operatorname{\mathbf{Spin}}(2n_{m}+1)$ not containing the center of
$\operatorname{\mathbf{Spin}}(2n_i+1)$ as a direct factor. We also find the
essential dimension of $G$ for each of the following cases, where either
$n_{i}=1$ for all $i$ or $m=2$, $n_{1}=1$, $2\leq n_{2}\leq 3$,
$\boldsymbol{\mu}$ is the diagonal central subgroup for both cases.
