Transmission between hosts is a critical part of the viral lifecycle. Recent studies of viral transmission have used genome sequence data to evaluate the number of particles transmitted between hosts, and the role of selection as it operates during the transmission process. However, the interpretation of sequence data describing transmission events is a challenging task. We here present a novel and comprehensive framework for using short-read sequence data to understand viral transmission events, designed for influenza virus, but adaptable to other viral species. Our approach solves multiple shortcomings of previous methods for this purpose; for example, we consider transmission as an event involving whole viruses, rather than sets of independent alleles. We demonstrate how selection during transmission and noisy sequence data may each affect naive inferences of the population bottleneck, accounting for these in our framework so as to achieve a correct inference. We identify circumstances in which selection for increased viral transmission may or may not be identified from data. Applying our method to experimental data in which transmission occurs in the presence of strong selection, we show that our framework grants a more quantitative insight into transmission events than previous approaches, inferring the bottleneck in a manner that accounts for selection, both for within-host virulence, and for inherent viral transmissibility. Our work provides new opportunities for studying transmission processes in influenza, and by extension, in other infectious diseases.