Given the advances in communication technologies and real-time traffic management, transit priority lanes are emerging as an indispensable component of intelligent transport systems. This scheme calls for giving priority to public transport. In this study, the question of interest is: Which roads can be nominated to give an exclusive lane to transit modes? Due to computational and theoretical complexities, the literature has yet to address this problem comprehensively at the network level considering various modes (public and private). Additionally, taking space away from private modes in favor of public transport may adversely affect the congestion level. To this end, inspired by the Braess Paradox, we seek mis-utilized space used by private modes to be dedicated to transit modes mainly on congested roads. To find such candidate roads, we define a merit index based on transit ridership and congestion level. The problem then becomes -to find the best subset of these candidate roads to cede a lane to transit mode. It is formulated as a bilevel mixedinteger, nonlinear programming problem in which the decision variables are binary (1: to cause the respective road to have an exclusive transit lane or 0: not). The adverse effects are minimized on the upper level represented by total travel time (public and private modes) spent on the network. The lower level accounts for a bimodal traffic assignment, to consider the impact of transit priority on private modes. We then develop an efficient low-RAM-intensity branch and bound as a solution algorithm. The search for the subset is made in such a way that improved public transport is achieved at zero cost to the overall performance of the network. A real dataset from the city of Winnipeg, Canada is used for numerical evaluations.