The connection between cognitive function and the “Big Five” personality traits (openness, conscientiousness, extraversion, agreeableness, and neuroticism) in the general population is well known; however, studies researching bipolar disorder (BD) are scarce. Therefore, this study aimed to investigate the Big Five as predictors of executive function, verbal memory, attention, and processing speed in euthymic individuals with BD (cross-sectional: n = 129, including time point t1; longitudinal: n = 35, including t1 and t2). Participants completed the NEO Five-Factor Inventory, the Color and Word Interference Test, the Trail Making Test, the d2 Test of Attention Revised, and the California Verbal Learning Test. The results showed a significant negative correlation between executive function and neuroticism at t1. Changes in cognitive function between t1 and t2 did not correlate with and could not be predicted by the Big Five at t1. Additionally, worse executive function at t2 was predicted by higher neuroticism and lower conscientiousness at t1, and high neuroticism was a predictor of worse verbal memory at t2. The Big Five might not strongly impact cognitive function over short periods; however, they are significant predictors of cognitive function. Future studies should include a higher number of participants and more time in between points of measurement.