While many bacterial pathogens are restricted to single host species, some have the capacity to undergo host switches, leading to the emergence of new clones that are a threat to human and animal health. However, the bacterial traits that underpin a multihost ecology are not well understood. Following transmission to a new host, bacterial populations are influenced by powerful forces such as genetic drift that reduce the fixation rate of beneficial mutations, limiting the capacity for host adaptation. Here, we implement a novel experimental model of bacterial host switching to investigate the ability of the multihost pathogen Staphylococcus aureus to adapt to new species under continuous population bottlenecks. We demonstrate that beneficial mutations accumulated during infection can overcome genetic drift and sweep through the population, leading to host adaptation. Our findings highlight the remarkable capacity of some bacteria to adapt to distinct host niches in the face of powerful antagonistic population forces.