Assigning RNA-seq reads to their transcript of origin is a fundamental task in transcript expression estimation. Where ambiguities in assignments exist due to transcripts sharing sequence, e.g. alternative isoforms or alleles, the problem can be solved through probabilistic inference. Bayesian methods have been shown to provide accurate transcript abundance estimates compared with competing methods. However, exact Bayesian inference is intractable and approximate methods such as Markov chain Monte Carlo and Variational Bayes (VB) are typically used. While providing a high degree of accuracy and modelling flexibility, standard implementations can be prohibitively slow for large datasets and complex transcriptome annotations.