Bioturbation refers to the transport processes carried out by living organisms and their physical effects on soils and sediments. It is widely recognized as an important mixing mechanism, particularly at the sediment-water interface in many natural systems. In order to quantify its impact on mixing, we propose a process-based model based on simple assumptions about organism burrowing behavior. Specifically, we consider burrowing events to be stochastic but memoryless, leading to exponential inter-burrow waiting times and depths. We then explore the impact of two different transport mechanisms on the vertical concentration distributions predicted by the model for a conservative (inert) tracer. We compare the results of our model to experimental data from a recent laboratory study of bioturbation by the freshwater oligochaete worm Lumbriculus variegatus, and find good quantitative agreement.