Bacteria have the ability to transfer certain small, mobilizable pieces of DNA from one cell to another, nearly regardless of species, through a process called conjugation. During conjugation, a donor cell containing a plasmid donates a copy to a recipient cell lacking a plasmid to form a transconjugant (a recipient cell now containing a plasmid). This has strong implications for the spread of antibiotic resistance among bacterial communities, as plasmids often harbor genes which confer resistance to certain antibiotics. Sharing of these plasmids between bacteria can increase the amount of resistant individuals in a population, which can produce infections that can be difficult to treat clinically. Therefore, having an accurate method to predict the rate at which these transconjugant cells form within a bacterial population can provide key insights to the spread of antibiotic resistance through plasmid-mediated gene transfer. Current models rely heavily on the presumed deterministic nature of transconjugant formation; however, we revealed that experiment estimates with these currently available methods can lead to biased estimates. In need of a more accurate and robust method to estimate the conjugation rate, we developed a novel stochastic model and accompanying lab protocol that effectively provides an accurate estimate of the conjugation rate. Our approach was inspired by the classic experiments of Luria and Delbrück, which revealed that mutation (changing a normal cell into a mutant cell type) was a stochastic process (i.e., random). Similarly, we hypothesized that this stochastic framework could be useful for creating a method for estimating conjugation (changing a recipient cell into a transconjugant cell type). We found using experiments and simulations that our method is accurate and robust under a variety of conditions. In conclusion, we developed a new method for the accurate estimation of plasmid conjugation rate.