MgB₂ in bulk form shows great promise as an inexpensive, light-weight alternative to bulk (RE)-Ba-Cu-O materials to act as trapped field magnets (TFMs), which can replace permanent magnets in applications such as desktop high-field magnet systems and rotating machines. In this paper, we investigate the thickness dependence of the trapped magnetic field in bulk MgB₂ superconductors. Two bulk MgB₂ samples, 20 mm in diameter and 10 mm in thickness, were fabricated using the powder-in-closed-tube (PICT) technique. The trapped field was then measured after field-cooled magnetisation for thicknesses of approximately 20 mm (both bulks stacked), 10 mm (single bulk), and then 7.5, 5, 4, 3, 2, 1.5 and 1 mm, for which the sample was machined down to the designated thickness using an automated-wet-polishing technique. A 2D axisymmetric finite-element model based on the H-formulation is used to simulate the experimental results and explain the observed thickness dependence of the trapped field. The numerical results assume a Jc(B) dependence based on the measured characteristics of small specimens taken from the bulk before and after machining. The Jc(B) measurements suggested a degradation of Jc occurred as the bulk was machined thinner and thinner: a decrease in Jc(0 T) of ~35% was observed between the pre- and post-machining specimens. Taking this into account in the models, by assuming a linear reduction in Jc with each machining process, reproduced the experimental results with very good agreement. Consistent trapped field measurements on the top and bottom surfaces suggest this degradation occurred globally, rather than local to the machined surface.