The global spread of invasive species may be facilitated by adaptation to the practices that humans use to manage those species. For example, marine invertebrates that adapt to metal-based antifouling biocides on ship hulls may be more likely to be introduced to and establish in metal-polluted environments. We tested this idea by studying clonal variation in tolerance to, and ability to recover from, exposure to copper in a widespread invasive marine bryozoan, Watersipora subtorquata. We cloned colonies of this organism to independently test multiple environments in a genotype by environment design, and then created a genetic variance–covariance matrix. Genotypes were exposed to a gradient of copper concentrations and growth measured during exposure and after a recovery period. There was a significant genotype × environment interaction in growth during exposure and recovery. We found clonal variation in tolerance and ability to recover from exposure to copper, with growth during exposure apparently trading off against growth after exposure. A weak genetic correlation between growth during and after exposure further indicated that they are separate traits. Overall, the genetic variation within this population indicates that there is considerable potential for adaptation to copper, but this comes at a cost to growth in unpolluted environments.