Based on head direction experiments in rats, the existence of localized bumps of thalamic activity has been proposed. We computationally demonstrate the existence of a novel class of localized bump solutions in a two-layer conductance-based thalamic network and analyze the mechanisms behind these stable patterns. In contrast to previous models of bump activity, here inhibition plays a crucial role in initially spreading neuronal firing and in subsequently sustaining it. In our model, we incorporate local strong, fast GABA(A) inhibition and diffuse weak, slow GABA(B) inhibition, based on previous biophysical experiments. These forms of inhibition contribute in different, yet complementary, ways to the observed pattern formation.