Providing passengers realizable and real-time information about bus arrivals as always plays an importance role for any bus agencies to keep their customers. In this paper, methods to define real-time prediction interval, bus on-time performance, and bus bunching detection are developed based on a proposal improvement model of non-parametric regression. The results of the model with APC and AVL data from OC Transpo have shown that it can provide information of bus arrival time and bus bunching with a given statistics significant in real-time. In addition, further applications of the developed model are discussed.