The vaginal microbiome (VMB) is a complex microbial community that is closely tied to reproductive health. Optimal VMB communities have compositions that are commonly defined by the dominance of certain Lactobacillus spp. and can remain stable over time or transition to non-optimal states dominated by anaerobic bacteria and associated with bacterial vaginosis (BV). The ability to remain stable or undergo transitions suggests a system with either single (mono-stable) or multiple (multi-stable) equilibrium states, though factors that contribute to stability have been difficult to determine due to heterogeneity in microbial growth characteristics and inter-species interactions. Here, we use a computational model to determine whether differences in microbial growth and interaction parameters could alter equilibrium state accessibility and account for variability in community composition after menses and antibiotic therapies. Using a global uncertainty and sensitivity analysis that captures parameter sets sampled from a physiologically relevant range, model simulations predicted that 79.7% of microbial communities were mono-stable (gravitate to one composition type) and 20.3% were predicted to be multi-stable (can gravitate to more than one composition type, given external perturbations), which was not significantly different from observations in two clinical cohorts (HMP cohort, 75.2% and 24.8%; Gajer cohort, 78.1% and 21.9%, respectively). The model identified key microbial parameters that governed equilibrium state accessibility, such as the importance of non-optimal anaerobic bacteria interactions with Lactobacillus spp., which is largely understudied. Model predictions for composition changes after menses and antibiotics were not significantly different from those observed in clinical cohorts. Lastly, simulations were performed to illustrate how this quantitative framework can be used to gain insight into the development of new combinatorial therapies involving altered prebiotic and antibiotic dosing strategies. Altogether, dynamical models could guide development of more precise therapeutic strategies to manage BV.