A change in the number of motor units that operate a particular muscle is an important indicator for the progress of a neuromuscular disease and the efficacy of a therapy. Inference for realistic statistical models of the typical data produced when testing muscle function is difficult, and estimating the number of motor units is an ongoing statistical challenge. We consider a set of models for the data, each with a different number of working motor units, and present a novel method for Bayesian inference based on sequential Monte Carlo. This provides estimates of the marginal likelihood and, hence, a posterior probability for each model. Implementing this approach in practice requires a sequential Monte Carlo method that has excellent computational and Monte Carlo properties. We achieve this by benefiting from the model's conditional independence structure, where, given knowledge of which motor units fired as a result of a particular stimulus, parameters that specify the size of each unit's response are independent of the parameters defining the probability that a unit will respond at all. The scalability of our methodology relies on the natural conjugacy structure that we create for the former and an enforced, approximate, conjugate structure for the latter. A simulation study demonstrates the accuracy of our method, and inferences are consistent across two different datasets arising from the same rat tibial muscle.