  We analyze the Bianchi I cosmology in the presence of a massless scalar field
and describe its dynamics via a semiclassical and quantum polymer approach. We
investigate the morphology of the emerging Big Bounce by adopting three
different sets of configurational variables: the natural Ashtekar connections,
the Universe volume plus two anisotropy coordinates and a set of anisotropic
volume-like coordinates (the latter two sets of variables would coincide in the
case of an isotropic Universe). In the semiclassical analysis we demonstrate
that the Big Bounce emerges in the dynamics for all the three sets of
variables. Moreover, when the Universe volume itself is considered as a
configurational variable, we have derived the polymer-modified Friedmann
equation and demonstrated that the Big Bounce has a universal nature, i.e. the
total critical energy density has a maximum value fixed by fundamental
constants and the Immirzi parameter only. From a pure quantum point of view, we
investigate the Bianchi I dynamics only in terms of the Ashtekar connections.
In particular, we apply the Arnowitt-Deser-Misner (ADM) reduction of the
variational principle and then we quantize the system. We study the resulting
Schr\"{o}dinger dynamics, stressing that the wave packet peak behavior over
time singles out common features with the semiclassical trajectories.
