Horizontal gene transfer (HGT) enables segments of DNA to be transferred between individuals in a population in addition to from parent to child. It is a prominent process in bacterial reproduction. Existing in silico models have succeeded in predicting when HGT will occur in evolving bacterial populations, and have utilised the concept of HGT in evolutionary algorithms. Here we present a genetic algorithm designed to model the process of bacterial evolution in a fitness landscape in which individuals with greater mutational robustness can outcompete those with higher fitness when a critical mutation rate (CMR) is exceeded. We show that the CMR has an exponential dependence on population size and can be lowered by HGT in both clonal and non-clonal populations. A population reproducing clonally has a higher CMR than one in which individuals undergo crossover. Allowing HGT only from donors with a non-zero fitness prevents HGT from lowering the CMR. In all cases the change in CMR with population size is greater for populations with 100 individuals or less. This represents a significant stage in bacterial evolution; smaller populations will exist when a population is founded or near to extinction. This will also be the case if a subset of the population is considered as a population in its own right, for example, the sub population of resistant bacteria that emerges due to the introduction of antibiotic resistance genes. Understanding the effect of mutation at such a critical stage is key to predicting the likely fate of a population.