The negative outcomes of experiencing workplace bullying are well documented, but a strong theoretical explanation for this has been relatively neglected. We draw on cognitive appraisal theory to suggest that individuals’ appraisals of and responses to negative acts at work will moderate the impact of said acts on wellbeing and performance outcomes. In a large study (N = 3,217) in Southeast Asia, we examine moderators in the form of (a) the extent to which individuals identify themselves as being bullied and (b) the coping strategies that individuals use to deal with negative acts. We find that these factors do moderate the impact of experiencing negative acts, in particular work-related negative acts. When individuals are subject to work-related negative acts but do not see themselves as being bullied they report higher levels of performance than those who do identify themselves as being bullied. Problem-focused coping was found to be effective for those sometimes targeted, but for persistent targets was detrimental to wellbeing. The present research has important implications for bullying research in examining factors that contribute to outcomes of bullying.