MgB_2 in bulk form shows great promise as trapped field magnets (TFMs) as an alternative to bulk (RE)BCO materials to replace permanent magnets in applications such as rotating machines, magnetic bearings and magnetic separation, and the relative ease of fabrication of MgB_2 materials has enabled a number of different processing techniques to be developed. In this paper, a comparison is made between bulk MgB_2 samples fabricated by the hot isostatic pressing (HIP), with and without Ti-doping, and infiltration growth (IG) methods and the highest trapped field in an IG-processed bulk MgB_2 sample, B_z = 2.12 at 5 K and 1.66 T at 15 K, is reported. Since bulk MgB_2 has a more homogeneous J_c distribution than (RE)BCO bulks, studies on such systems are made somewhat easier because simplified assumptions regarding the geometry and J_c distribution can be made, and a numerical simulation technique based on the 2D axisymmetric H-formulation is introduced to model the complete process of field cooling (FC) magnetization. As input data for the model, the measured J_c(B,T) characteristics of a single, small specimen taken from each bulk sample are used, in addition to measured specific heat and thermal conductivity data for the materials. The results of the simulation reproduce the experimental results extremely well: (1) indicating the samples have excellent homogeneity, and (2) validating the numerical model as a fast, accurate and powerful tool to investigate the trapped field profile of bulk MgB_2 discs of any size accurately, under any specific operating conditions. Finally, the paper is concluded with a numerical analysis of the influence of the dimensions of the bulk sample on the trapped field.