Many animal behaviors require orientation and steering with respect to the environment. For insects, a key brain area involved in spatial orientation and navigation is the central complex. Activity in this neural circuit has been shown to track the insect's current heading relative to its environment and has also been proposed to be the substrate of path integration. However, it remains unclear how the output of the central complex is integrated into motor commands. Central complex output neurons project to the lateral accessory lobes (LAL), from which descending neurons project to thoracic motor centers. Here, we present a computational model of a simple neural network that has been described anatomically and physiologically in the LALs of male silkworm moths, in the context of odor-mediated steering. We present and analyze two versions of this network, one rate based and one based on spiking neurons. The modeled network consists of an inhibitory local interneuron and a bistable descending neuron (flip-flop) that both receive input in the LAL. The flip-flop neuron projects onto neck motor neurons to induce steering. We show that this simple computational model not only replicates the basic parameters of male silkworm moth behavior in a simulated odor plume but can also take input from a computational model of path integration in the central complex and use it to steer back to a point of origin. Furthermore, we find that increasing the level of detail within the model improves the realism of the model's behavior, leading to the emergence of looping behavior as an orientation strategy. Our results suggest that descending neurons originating in the LALs, such as flip-flop neurons, are sufficient to mediate multiple steering behaviors. This study is therefore a first step to close the gap between orientation circuits in the central complex and downstream motor centers.