Bullying in social media such as Twitter and Facebook has been recognised as a serious issue in Indonesia. Bullying in social media is a type of human rights violation that involves other people following an initial perpetrator in sending bullying messages repeatedly and intentionally in order to cause distress and risk to the victims. Moreover, some people use Twitter for different, more innocuous, but still unpleasant, purposes such as embarrassing someone. Our research analyses Indonesian bullying words on Twitter so as to discover Indonesian bullying patterns. It also discusses how to mine Indonesian bullying words on Twitter by using text mining techniques. Analysing Indonesian bullying words is one of the challenges in this work. Our research has successfully identified that "bangsat" and "anjing" terms are the trend of Indonesian bullying patterns on Twitter. This work also compares Indonesian bullying patterns in Jakarta and Surabaya. The results are quite similar. The "bangsat" and "anjing" terms usually occur on Twitter located in both cities. Finally, our research discusses how text mining could provide a solution towards analysing Indonesian bullying words patterns in Twitter messages.