The introduction of invasive species to new locations (that is, biological invasions) can have major impact on biodiversity, agriculture and public health. As such, determining the routes and modality of introductions with genetic data has become a fundamental goal in molecular ecology. To assist with this goal, new statistical methods and frameworks have been developed, such as approximate Bayesian computation (ABC) for inferring invasion history. Here, we present a model of invasion accounting for multiple introductions from a single source (MISS), a heretofore largely unexplored model. We simulate microsatellite data to evaluate the power of ABC to distinguish between single and multiple introductions from the same source, under a range of demographic parameters. We also apply ABC to microsatellite data from three invasions of bumblebee in New Zealand. In addition, we assess the performance of several methods of summary statistics selection. Our simulated results suggested good ability to distinguish between one- and two-wave models over much but not all of the parameter space tested, independent of summary statistics used. Globally, parameter estimation was good except for bottleneck timing. For one of the bumblebee species, we clearly rejected the MISS model, while for the other two we found inconclusive results. Since a second wave may provide genetic reinforcement to initial colonists, help relieve inbreeding among founders, or increase the hazard of the invasion, its detection may be crucial for managing invasions; we suggest that the MISS model could be considered as a potential model in future theoretical and empirical studies of invasions.