Free-hand dental procedures are typically repetitive, time-consuming and require high precision and manual dexterity. Robots can play a key role in improving procedural accuracy and safety, enhancing patient comfort, and reducing operator workload. However, robotic solutions for free-hand procedures remain limited or completely lacking. To address this gap, we develop a haptic bilateral teleoperation system (HBTS) for free-hand dental procedures (FH-HBTS). The system includes a mechanical end-effector, compatible with standard clinical tools, and equipped with an endoscopic camera for improved visibility of the intervention site. By ensuring motion and force correspondence between the operator's and the robot's actions, monitored through visual feedback, we enhance the operator's sensory awareness and motor accuracy. Furthermore, to ensure procedural safety, we limit interaction forces by scaling the motion references provided to the admittance controller based solely on measured contact forces. This ensures effective force limitation in all contact states without requiring prior knowledge of the environment. The proposed FH-HBTS is validated both through a technical evaluation and an in-vitro pre-clinical study conducted on a dental model under clinically representative conditions. The results show that the system improves the naturalness, safety, and accuracy of teleoperation, highlighting its potential to enhance free-hand dental procedures.