To investigate the dynamical properties of the novel hybrid compound, lithium benzimidazolate-borohydride Li2(bIm)BH4 (where bIm denotes a benzimidazolate anion, C7N2H5 -), we have used a set of complementary techniques: neutron powder diffraction, ab initio density functional theory calculations, neutron vibrational spectroscopy, nuclear magnetic resonance, neutron spin echo, and quasi-elastic neutron scattering. Our measurements performed over the temperature range from 1.5 to 385 K have revealed the exceptionally fast low-temperature reorientational motion of BH4 - anions. This motion is facilitated by the unusual coordination of tetrahedral BH4 - anions in Li2(bIm)BH4: each anion has one of its H atoms anchored within a nearly square hollow formed by four coplanar Li+ cations, while the remaining -BH3 fragment extends into a relatively open space, being only loosely coordinated to other atoms. As a result, the energy barriers for reorientations of this fragment around the anchored B-H bond axis are very small, and at low temperatures, this motion can be described as rotational tunneling. The tunnel splitting derived from the neutron spin echo measurements at 3.6 K is 0.43(2) μeV. With increasing temperature, we have observed a gradual transition from the regime of low-temperature quantum dynamics to the regime of classical thermally activated jump reorientations. The jump rate of the uniaxial 3-fold reorientations reaches 5 × 1011 s-1 at 80 K. Nearer room temperature and above, both nuclear magnetic resonance and quasielastic neutron scattering measurements have revealed the second process of BH4 - reorientations characterized by the activation energy of 261 meV. This process is several orders of magnitude slower than the uniaxial 3-fold reorientations; the corresponding jump rate reaches ~7 × 108 s-1 at 300 K.