Finite mixture models are a popular approach for unsupervised machine learning tasks. Mixtures of factor analyzers assume a latent variable structure, thereby modelling the data in a lower-dimensional space. Herein, we augment the traditional alternating expectation conditional maximization algorithm by incorporating the non-parametric bootstrap during the parameter estimation process. This augmentation is shown to improve discovery of both the true number of groups and the true latent dimensionality through simulations, while also showing superior clustering performance on benchmark data sets.