Directional properties of ultrafast laser-based hard x-ray sources are experimentally studied using tightly focused approximately millijoule laser pulses incident on a bulk Mo target. Energy distributions of Kα and total x rays, as well as source-size distributions are directionally resolved in vacuum and in flowing helium, respectively. Directional distributions of x-ray emission is more isotropic for p-polarized pump than for s-polarized. Based on source-size measurements, a simple two-location model, with expanded plasma and bulk material, is employed to represent the x-ray source profile.