In the recent times, the race to cope with the increasing multidrug resistance of pathogenic bacteria has lost much of its momentum and health professionals are grasping for solutions to deal with the unprecedented resistance levels. As a result, there is an urgent need for a concerted effort towards the development of new antimicrobial drugs to stay ahead in the fight against the ever adapting bacteria. In the present report, antibacterial classification functions (models) based on the topological molecular computational design-computer aided "rational" drug design (TOMOCOMD-CARDD) atom-based non-stochastic and stochastic bilinear indices are presented. These models were built using the linear discriminant analysis (LDA) method over a balanced chemical compounds dataset of 2230 molecular structures, with a diverse range of structural and molecular mechanism modes. The results of this study indicated that the non-stochastic and stochastic bilinear indices provided excellent classification of the chemical compounds (with accuracies of 86.31% and 84.92%, respectively, in the training set). These models were further externally validated yielding correct classification percentages of 86.55% and 87.91% for the non-stochastic and stochastic bilinear models, respectively. Additionally, the obtained models were compared with those reported in the literature and demonstrated comparable results, although the latter were built over much smaller datasets and with much higher degrees of freedom. Finally, simulated ligand-based virtual screening of 116 compounds, recently identified as potential antibacterials, was performed yielding 86.21% and 83.62% of correct classification, respectively, and thus demonstrating the utility of the obtained TOMOCOMD-CARDD models in the search of novel compounds with desirable antibacterial activity.