Discriminative training techniques define state-of-the-art performance for automatic speech recognition systems. However, they are inherently prone to overfitting, leading to poor generalization performance when using limited training data. In order to address this issue, this paper presents a full Bayesian framework to account for model uncertainty in sequence discriminative training of factored TDNN acoustic models. Several Bayesian learning based TDNN variant systems are proposed to model the uncertainty over weight parameters and choices of hidden activation functions, or the hidden layer outputs. Efficient variational inference approaches using a few as one single parameter sample ensure their computational cost in both training and evaluation time comparable to that of the baseline TDNN systems. Statistically significant word error rate (WER) reductions of 0.4%-1.8% absolute (5%-11% relative) were obtained over a state-of-the-art 900 hour speed perturbed Switchboard corpus trained baseline LF-MMI factored TDNN system using multiple regularization methods including F-smoothing, L2 norm penalty, natural gradient, model averaging and dropout, in addition to i-Vector plus learning hidden unit contribution (LHUC) based speaker adaptation and RNNLM rescoring. Consistent performance improvements were also obtained on a 450 hour HKUST conversational Mandarin telephone speech recognition task. On a third cross domain adaptation task requiring rapidly porting a 1000 hour LibriSpeech data trained system to a small DementiaBank elderly speech corpus, the proposed Bayesian TDNN LF-MMI systems outperformed the baseline system using direct weight fine-tuning by up to 2.5\% absolute WER reduction.