Transmission of HIV strains with drug-resistance mutations (DRMs) causes public health problems in resource-rich countries. We use a stochastic model, with data from viral competition experiments, to analyze the effect of fitness costs (FCs) and genetic bottlenecks on limiting transmission of 10 clinically significant DRMs. Transmission of DRMs with low FCs (∼0.2%) is similar to wild-type; transmission chains last ∼8 generations causing clusters of ∼60 infected individuals. Genetic bottlenecks substantially limit transmission of DRMs with moderately high FCs (∼0.6%); chains last ∼1-3 generations with transmission clusters of 2-7. Transmission of DRMs with extremely high FCs (>6%) only occurs from ∼5% of index cases. DRMs can revert to wild-type and remain as minority strains, within treatment-naïve individuals, undetectable by current resistance assays. We calculate, based on assay sensitivity, the length of time each DRM is detectable within individuals. Taken together, our results imply a hidden epidemic of transmitted resistance may exist.