  We study selection principles related to bornological covers using the notion
of ideals. We consider ideals $\mathcal I$ and $\mathcal J$ on $\omega$ and
standard ideal orderings $KB, K$. Relations between cardinality of a base of a
bornology with certain selection principles related to bornological covers are
established using cardinal invariants such as modified pseudointersection
number, the unbounding number and slaloms numbers. When $\mathcal I
\leq_\square \mathcal J$ for ideals $\mathcal I, \mathcal J$ and $\square\in
\{1\text{-}1,KB,K\}$, implications among various selection principles related
to bornological covers are established. Under the assumption that ideal
$\mathcal I$ has a pseudounion we show equivalences among certain selection
principles related to bornological covers. Finally, the $\mathcal
I\text{-}\mathfrak B^s$-Hurewicz property of $X$ is investigated. We prove that
$\mathcal I\text{-}\mathfrak B^s$-Hurewicz property of $X$ coincides with the
$\mathfrak B^s$-Hurewicz property of $X$ if $\mathcal I$ has a pseudounion.
Implications or equivalences among selection principles, games and $\mathcal
I\text{-}\mathfrak B^s$-Hurewicz property which are obtained from our
investigations are described in diagrams.
