Invasive species often undergo demographic bottlenecks that cause a decrease in genetic diversity and associated reductions in population fitness. Despite this, they manage to thrive in novel environments. Investigating the effects of inbreeding and genetic bottlenecks on population fitness for invasive species is, therefore, key to understanding how they may survive in new environments. We used the blowfly Calliphora vicina (Sciences, Mathématiques et Physique, 1830, 2, 1), which is native to Europe and was introduced to Australia and New Zealand, to examine the effects of genetic diversity on population fitness. We first collected 59 samples from 15 populations across New Zealand and one in Australia, and used 20,501 biallelic SNPs to investigate population genomic diversity, structure and admixture. We then explored the impacts of repeated experimental bottlenecks on population fitness by creating inbred and outbred lines of C. vicina and measuring a variety of fitness traits. In wild‐caught samples, we found low overall genetic diversity, signals of genetic admixture and limited (<3%) genetic differentiation between North and South Island populations, with genetic links between the South Island and Australia. Following experimental bottlenecks, we found significant reductions in fitness for inbred lines. However, fitness effects were not felt equally across all phenotypic traits. Moreover, they were not enough to cause population collapse in any experimental line, suggesting that C. vicina (when under relaxed selection, as in laboratory settings) may be able to compensate for population bottlenecks even when highly inbred. Our results demonstrate the value of a tractable experimental system for investigating processes that may facilitate or hamper biological invasion.