Genetic background has the potential to influence both the tempo and trajectory of adaptive change: Different genotypes of a given species may adopt varied solutions to the same environmental challenge, or they may approach the same solution at different rates. Laboratory selection has been widely used to experimentally examine the evolutionary consequences of variation in genetic background, although largely using genotypes differing by only a few mutations. Here, we leverage natural variation in the bacterium Pseudomonas aeruginosa to investigate whether different adaptive solutions are accessible from distant points of departure on an adaptive landscape. We evolved 17 diverse genotypes in a laboratory medium that partially mimics the lung sputum of cystic fibrosis patients, and we measured changes in 10 phenotypes as well as in fitness. Using phylogenetically informed analyses, we found that genetic background impacted the tempo, but not the trajectory, of phenotypic evolution: Different starting genotypes converged toward similar phenotypes, but at varying rates. Our findings add to a growing body of evidence supporting widespread diminishing return epistasis during adaptation. The importance of genetic background toward the trajectory of adaptation remains inconsistent across experimental systems and conditions.