Variational Bayes (VB), a method originating from machine learning, enables fast andscalable estimation of complex probabilistic models. Thus far, applications of VB indiscrete choice analysis have been limited to mixed logit models with unobserved inter-individual taste heterogeneity. However, such a model formulation may be too restrictivein panel data settings, since tastes may vary both between individuals as well as acrosschoice tasks encountered by the same individual. In this paper, we derive a VB methodfor posterior inference in mixed logit models with unobserved inter- and intra-individualheterogeneity. In a simulation study, we benchmark the performance of the proposed VBmethod against maximum simulated likelihood (MSL) and Markov chain Monte Carlo(MCMC) methods in terms of parameter recovery, predictive accuracy and computationalefficiency. The simulation study shows that VB can be a fast, scalable and accurate alter-native to MSL and MCMC estimation, especially in applications in which fast predictionsare paramount. VB is observed to be between 2.8 and 17.7 times faster than the twocompeting methods, while affording comparable or superior accuracy. Besides, the sim-ulation study demonstrates that a parallelised implementation of the MSL estimator withanalytical gradients is a viable alternative to MCMC in terms of both estimation accuracyand computational efficiency, as the MSL estimator is observed to be between 0.9 and 2.1times faster than MCMC.