Using in situ low-energy electron microscopy and density functional theory, we studied the growth structure and work function of bilayer graphene on Pd(111). Low-energy electron diffraction analysis established that the two graphene layers have multiple rotational orientations relative to each other and the substrate plane. We observed heterogeneous nucleation and simultaneous growth of multiple, faceted layers prior to the completion of second layer. We propose that the facetted shapes are due to the zigzag-terminated edges bounding graphene layers growing under the larger overlying layers. We also found that the work functions of bilayer graphene domains are higher than those of monolayer graphene, and depend sensitively on the orientations of both layers with respect to the substrate. Based on first-principles simulations, we attribute this behavior to oppositely oriented electrostatic dipoles at the graphene/Pd and graphene/graphene interfaces, whose strengths depend on the orientations of the two graphene layers.