Dublin Anti-Bullying Self-Efficacy Scales aim to measure the effectiveness of school anti-bullying programs in promoting five steps that victims and bystanders take against online and offline bullying behaviors. These steps are anti-bullying self-efficacy beliefs to recognize bullying behaviors, comprehend emergency, take responsibility, know what to do, and intervene. However, when an anti-bullying program is very effective for the majority of participants who give high scores, a considerable number of participants who give low scores are very likely to be detected as outliers. This raises two measurement issues. First, high scores create highly negatively skewed data and lead to measuring a unidimensional rather than multidimensional construct. This could be one reason why recent research has been unclear about the extent to which the scales measure a unidimensional, multidimensional, or bifactor construct. Second, should outliers be removed or be considered as participants for whom the program was ineffective? If the scales had measurement invariance across the group of outliers and nonoutliers or low and high self-efficacy, it could be concluded that the antibullying program was ineffective for some participants. The current research aims to address these issues by testing both measurement invariance as well as unidimensional and bifactor models of anti-bullying self-efficacy. Results of Pure Exploratory Bifactor (PEBI) Analyses and Item Response Theory (IRT) with Two-Parameter-Logistic (2PL) Models of data from a convenience sample of 14-year-old students in Ireland (N=1,222) indicated sufficient psychometric properties of both unidimensional and multidimensional scales for victim offline, victim online, bystander offline, and bystander online. Further research can use these scales for measuring the bifactor model of anti-bullying self-efficacy as well as the cut-off score for distinguishing between low and high anti-bullying self-efficacy.