  We show that it is possible to realize a cosmological bouncing solution in an
anisotropic but homogeneous Bianchi-I background in a class of non-local,
infinite derivative theories of gravity. We show that the anisotropic shear
grows slower than in general relativity during the contraction phase, peaks to
a finite value at the bounce point, and then decreases as the universe
asymptotes towards isotropy and homogeneity, and ultimately to de Sitter. Along
with a cosmological constant, the matter sector required to drive such a bounce
is found to consist of three components - radiation, stiff matter and
$k$-matter (whose energy density decays like the inverse square of the average
scale factor). Generically, $k$-matter exerts anisotropic pressures. We will
test the bouncing solution in local and non-local gravity and show that in the
latter case it is possible to simultaneously satisfy positivity of energy
density and, at least in the late time de Sitter phase, avoid the introduction
of propagating ghost/tachyonic modes.
