Cyberbullying has become one of the most pressing online risks for adolescents and has raised serious concerns in society. Recent years have witnessed a surge in research aimed at developing principled learning models to detect cyberbullying behaviors. These efforts have primarily focused on building a single generic classification model to differentiate bullying content from normal (non-bullying) content among all users. These models treat users equally and overlook idiosyncratic information about users that might facilitate the accurate detection of cyberbullying. In this paper, we propose a personalized cyberbullying detection framework, PI-Bully, that draws on empirical findings from psychology highlighting unique characteristics of victims and bullies and peer influence from like-minded users as predictors of cyberbullying behaviors. Our framework is novel in its ability to model peer influence in a collaborative environment and tailor cyberbullying prediction for each individual user. Extensive experimental evaluations on real-world datasets corroborate the effectiveness of the proposed framework.