Traffic incidents such as accidents or vehicle breakdowns are one of the major causes of traffic congestion in urban areas. Consequently, accurate prediction of duration of these incidents is considered as one of the most important challenges by traffic management authorities. Although data-driven regression methods can predict the duration of these incidents with reasonable precision. However, the prediction performance may vary considerably from one to another. Hence, it is important to provide some measure of confidence associated with the forecast duration of the incidents. Such measures can prove to be highly useful in planning real-time response. To address this issue, we propose Bayesian Support Vector Regression (BSVR), which gives error bars as the measurement of uncertainty along with the predicted duration of incidents. We also evaluate sensitivity and specificity for different error tolerance limit to assess the performance of BSVR.