  A hybrid (hydrodynamics + hadronic transport) theoretical framework is
assembled to model the bulk dynamics of relativistic heavy-ion collisions at
energies accessible in the Beam Energy Scan (BES) program at the Relativistic
Heavy-Ion Collider (RHIC) and the NA61/SHINE experiment at CERN. The system's
energy-momentum tensor and net baryon current are evolved according to
relativistic hydrodynamics with finite shear viscosity and non-zero net baryon
diffusion. Our hydrodynamic description is matched to a hadronic transport
model in the dilute region. With this fully integrated theoretical framework,
we present a pilot study of the hadronic chemistry, particle spectra, and
anisotropic flow. Phenomenological effects of a non-zero net-baryon current and
its diffusion on hadronic observables are presented for the first time. The
importance of the hadronic transport phase is also investigated.
