Over 600,000 bridges in the U.S. must be inspected every two years to identify flaws, defects, or potential problems that may need follow-up maintenance. Bridge inspection has adopted unmanned aerial vehicles (or drones) for improving safety, efficiency, and cost-effectiveness. Although drones can operate in an autonomous mode, keeping inspectors in the loop is critical for complex tasks in bridge inspection. Therefore, inspectors need to develop the skill and confidence to operate drones in their jobs. This paper presents the design and development of a virtual reality-based training and assessment system for inspectors assisted by a drone in bridge inspection. The system is composed of four integrated modules: a simulated bridge inspection developed in Unity, an interface that allows a trainee to operate the drone in simulation using a remote controller, data monitoring and analysis to provide real-time, in-task feedback to trainees to assist their learning, and a post-study assessment supporting personalized training. The paper also conducts a proof-of-concept pilot study to illustrate the functionality of this system. The study demonstrated that TASBID, as a tool for the early-stage training, can objectively identify the training needs of individuals in detail and, further, help them develop the skill and confidence in collaborating with a drone in bridge inspection. The system has built a modeling and analysis platform for exploring advanced solutions to the human-drone cooperative inspection of civil infrastructure.