Brassica vegetables are bitter, predominantly because they contain bitter-tasting glucosinolates. Individuals with high bitter taste sensitivity are reported to have lower consumption of bitter vegetables. Studies reported that cooking methods can alter the sensory characteristics of vegetables, increasing acceptability. This study investigated consumer liking of turnip cooked by four methods (boiled-pureed, roasted, steamed-pureed and stir-fried) and related this to sensory characteristics. Additionally, this study examined the effect of the bitter taste genotype on taste perception and liking of the cooked turnip samples. Participants (n = 74) were recruited and the TAS2R38 genotype was measured. Liking, consumption intent, perception of bitterness and sweetness of turnip were evaluated. A sensory profile of the cooked turnip variants was also determined by a trained sensory panel. There were significant differences in the overall (p = 0.001) and taste (p = 0.002) liking between cooking methods. Turnip liking was increased when preparation led to sweeter taste profiles. The TAS2R38 genotype had a significant effect on bitter perception (p = 0.02) but did not significantly affect taste liking. In conclusion, the cooking method affected turnip liking, and the bitter perception in turnip was influenced by the TAS2R38 genotype. However, taste sensitivity did not predict turnip liking in this UK adult cohort.