Availability of the big data from Bluetooth MAC Scanners (BMS) over the network provides opportunities to trace the movement of the individual Bluetooth-equipped vehicles on the network. However, BMS might not perfectly detect all the devices within its detection zone. For dense urban networks, the scanner scanning zones can significantly overlap, which complicates the detailed reconstruction of the vehicle trajectory. Addressing the need, this paper proposes a Slit based Trajectory Reconstruction (STATER) algorithm where for each BMS, a slit is defined that considers the overlap and connectivity with other BMS, and thereafter the trajectory is reconstructed considering the shortest path over the observed sequence of slits. A numerical simulation framework is proposed to thoroughly test the proposed STATER algorithm at various levels of ambiguity and randomness in the input dataset. The testing results indicate that the reconstructed trajectories could capture more than 90% (true positive) of the actual path and an average error (false positive) of 11.3% at different randomness levels considered in the experiments. As proof of concept, STATER is applied on one-day data from the entire Brisbane network with 0.56m trips, the computational performance for which supports its practical applicability.