Accurate estimation of hydrodynamic drag experienced during locomotion is an important parameter for the study of dolphin swimming biomechanics. Model based approaches have been used to estimate drag force. However, kinematic data for these estimates tends to be limited to a relatively small number of swimming events. This work estimates drag acting on a gliding bottlenose dolphin (Tursiops truncatus) using a dynamic model of the animal motion and tag based measurements of swimming kinematics. A data driven approach was used to mine qualified animal gliding segments from 84 hours of biologging tag data from three animals. Using this approach, we were able to identify 532 gliding events over a range of swimming speeds (1 m/s to 5 m/s), an order of magnitude more data than some comparable studies in the literature. The identified drag coefficients cover a wide range of speeds and compare well with other published results. Importantly, the results indicate that swimming dolphins could experience 2.1 times more drag during low amplitude fluking than gliding at the Reynolds number of 4.263 x 10^6 (equivalent to traveling speed of 1.8 m/s with animal body length of 2.5 m), which speaks to the energetic benefits of employing a fluke-and-glide gait pattern as opposed to continuous fluking. While this work presents results from bottlenose dolphin swimming data, the method can be applied to other cetaceans in various environments as long as speed can be measured/estimated accurately.