In recent years, the problem of bus travel time prediction is becoming more important for applications such as informing passengers regarding the expected bus arrival time in order to make public transit more attractive to the urban commuters. One of the popular techniques reported for such prediction is the use of time series analysis. Most of the studies on the application of time series techniques for bus arrival time prediction used Box-Jenkins AutoRegressive Integrated Moving Average (ARIMA) models, which are presently not suited for real time implementation. This is mainly due to the necessity and dependence of ARIMA models on a time series modelling software to execute. Moreover, the ARIMA model building process is time consuming, making it difficult to use for real-time implementations. Alternatively, Exponential Smoothing (ES) methods can be used, as they are easy to understand and implement when compared to ARIMA models. The present study is an attempt in this direction, where the basic equation of ES is used, as the state equation with Kalman filtering to recursively update the travel time estimate as the new observation becomes available. The proposed algorithm of state space formulation of ES with Kalman filtering for bus travel time and arrival time prediction was field tested using 105 actual bus trips data along a particular bus route from Chennai, India. The results are promising and a comparison of the proposed algorithm with ES alone without state space formulation and Kalman filtering has also been performed. An information system based on a webpage for real-time display of bus arrival times has been designed and developed using the proposed algorithm.