Bus Signal Priority (BSP) is an operational strategy to reduce the delay experienced by a bus at a signalised intersection. As a bus is detected, the signal timings are adjusted to allow the bus to pass through the intersection without having to experience much delay. To help in providing this priority, the time of bus crossing at the intersection stop bar needs to be predicted. This study tries to predict the stop bar crossing time by analysing realistic manoeuvres encountered by a bus as it approaches an intersection and then developing prediction models for the identified manoeuvres using kinematic equations of motion and driver behaviour. Three manoeuvres were identified as part of the study, and the prediction model was evaluated based on the simulation results obtained. The prediction was applied when the bus was detected 500m, 400m, 300m, 200m, and 100m away from the intersection stop bar. The error range for prediction done at 100m from stop bar is -0.29 to +0.17 sec for manoeuvre (i), -2.99 to +2.21 sec to for manouevre (ii) and, +0.09 to +3.04 sec for manouevre (iii), indicating the proposed methodology as a viable option for accurate prediction of bus arrival time at the stop bar near signalized intersections