A trust-based mixed-initiative scheme for the bilateral teleoperation of mobile robotic systems is proposed. In a mixed-initiative control scheme, the control task is shared between human and an in-situ autonomous robot controller. In a bilateral haptic teleoperation scheme, a human operator controls a robot remotely through some control device while receiving haptic force feedback cues. The bilateral haptic teleoperation is implemented with mixed-initiative control, by introducing computational two-way trust models, to increase the performance of the joint system. Mixed-initiative is enabled by scaling the manual and autonomous control inputs with a function of computational human-to-robot trust. The haptic force feedback is dynamically scaled with a function of computational robot-to-human trust and hence reduces the physical workload of operator. Passivity based techniques are developed for the proposed control scheme in the presence of such time-varying scales as well as communication delays. The trust-based mixed-initiative teleoperation scheme has been experimentally tested. The results indicate the effectiveness of our proposed scheme in improving task performance by 31% and reducing operator workload by 23.9% compared to the exclusively bilateral teleoperation.