Patient-specific finite element (FE) models of bone require the assignment of heterogeneous material properties extracted from the subject's computed tomography (CT) images. Though node-based (NB) and element-based (EB) material mapping methods (MMMs) have been proposed, the sensitivity and convergence of FE models to MMM for varying mesh sizes are not well understood. In this work, CT-derived and synthetic bone material data were used to evaluate the effect of MMM on results from FE analyses. Pelvic trabecular bone data was extracted from CT images of six subjects, while synthetic data were created to resemble trabecular bone properties. The numerical convergence of FE bone models using different MMMs were evaluated for strain energy, von-Mises stress, and strain. NB and EB MMMs both demonstrated good convergence regarding total strain energy, with the EB method having a slight edge over the NB. However, at the local level (e.g., maximum stress and strain), FE results were sensitive to the field type, MMM, and the FE mesh size. The EB method exhibited superior performance in finer meshes relative to the voxel size. The NB method converged better than did the EB method for coarser meshes. These findings may lead to higher-fidelity patient-specific FE bone models.