Step 1: Remember what molecularity actually counts.
Molecularity simply counts how many reacting species, whether atoms, molecules or ions, must physically come together and collide in one single elementary step for that step to occur. It is a theoretical head count, not something measured experimentally.
Step 2: Look only at Step II in isolation.
Step II is written as $H_2O_2 + IO^- \rightarrow H_2O + I^- + O_2$. On the left-hand side, exactly two species are colliding to react, one molecule of $H_2O_2$ and one ion of $IO^-$.
Step 3: Count them up.
Since two species must collide simultaneously for this elementary step to happen, the molecularity of Step II is two, it is bimolecular.
\[ \boxed{\text{Molecularity of Step II} = 2} \]