  We study classical configurations in the ${\mathbb C}P^{N-1}$ model on
${\mathbb R}^{1}\times S^{1}$ with twisted boundary conditions. We focus on
specific configurations composed of multiple fractionalized-instantons, termed
"neutral bions", which are identified as "perturbative infrared renormalons" by
\"{U}nsal and his collaborators. For ${\mathbb Z}_N$ twisted boundary
conditions, we consider an explicit ansatz corresponding to topologically
trivial configurations containing one fractionalized instanton ($\nu=1/N$) and
one fractionalized anti-instanton ($\nu=-1/N$) at large separations, and
exhibit the attractive interaction between the instanton constituents and how
they behave at shorter separations. We show that the bosonic interaction
potential between the constituents as a function of both the separation and $N$
is consistent with the standard separated-instanton calculus even from short to
large separations, which indicates that the ansatz enables us to study bions
and the related physics for a wide range of separations. We also propose
different bion ansatze in a certain non-${\mathbb Z}_{N}$ twisted boundary
condition corresponding to the "split" vacuum for $N= 3$ and its extensions for
$N\geq 3$. We find that the interaction potential has qualitatively the same
asymptotic behavior and $N$-dependence as those of bions for ${\mathbb Z}_{N}$
twisted boundary conditions.
