Thin Bi(110) films deposited on highly oriented pyrolytic graphite (HOPG) exhibit a pronounced moire pattern; here the origin of the moire pattern is investigated using scanning tunneling microscopy (STM) and spectroscopy (STS), high-resolution transmission electron microscopy (HR-TEM), and density functional theory (DFT). It is shown that the moire pattern forms only on islands which are misoriented by ∼30◦ with respect to the usual substrate symmetry direction. Two models of the moire pattern are presented: (i) a commensurate monolayer construction (CMC) for rectangular overlayer symmetry on hexagonal substrates and (ii) a qualitative model based on simple superposition of a Bi overlayer on graphene. The CMC model has previously been applied only to systems with pure hexagonal symmetry. Both models generate moire patterns with key parameters (period, angles of the pattern measured with respect to the main HOPG and Bi crystal directions) that are consistent with the experimental results, but development of a fully predictive/quantitative model remains an outstanding challenge. The electronic structure of the moire pattern is investigated using STS and DFT, and it is found that the local density of states (LDOS) is modulated by the moire pattern. These results are consistent with a picture in which a small distortion of Bi atomic positions at the film-substrate interface results in periodic modulation of the LDOS, hence allowing observation of the moire pattern in STM images.