  We present a multi-passband photometric study of the Blue Straggler Star
(BSS) population in the Galactic globular cluster (GC) NGC\,1261, using
available space- and ground-based survey data.~The inner BSS population is
found to have two distinct sequences in the color-magnitude diagram, similar to
double BSS sequences detected in other GCs. These well defined sequences are
presumably linked to single short-lived events such as core collapse, which are
expected to boost the formation of BSSs.~In agreement with this, we find a BSS
sequence in NGC\,1261 which can be well reproduced individually by a
theoretical model prediction of a 2 Gyr old population of stellar collision
products, which are expected to form in the denser inner regions during
short-lived core contraction phases.~Additionally, we report the occurrence of
a group of BSSs with unusually blue colours in the CMD, which are consistent
with a corresponding model of a 200 Myr old population of stellar collision
products.~The properties of the NGC\,1261 BSS populations, including their
spatial distributions, suggest an advanced dynamical evolutionary state of the
cluster, but the core of this GC does not show the classical signatures of
core-collapse.~We argue these apparent contradictions provide evidence for a
post-core-collapse bounce state seen in dynamical simulations of old GCs.
