  The semiconductor ReSe$_2$ is characterized by a strongly anisotropic optical
absorption and is therefore promising as an optically active component in
two-dimensional heterostructures. However, the underlying femtosecond dynamics
of photoinduced excitations in such materials has not been sufficiently
explored. Here, we apply an infrared optical excitation to single-layer
ReSe$_2$ grown on a bilayer graphene substrate and monitor the temporal
evolution of the excited state signal using time- and angle-resolved
photoemission spectroscopy. We measure an optical gap of $(1.53 \pm 0.02)$ eV,
consistent with resonant excitation of the lowest exciton state. The exciton
distribution is tunable via the linear polarization of the pump pulse and
exhibits a biexponential decay with time constants given by $\tau_1 = (110 \pm
10)$ fs and $\tau_2 = (650 \pm 70)$ fs, facilitated by recombination via an
in-gap state that is pinned at the Fermi level. By extracting the
momentum-resolved exciton distribution we estimate its real-space radial extent
to be greater than 17.1 \AA, implying significant exciton delocalization due to
screening from the bilayer graphene substrate.
