Research on the sixth generation cellular networks (6G) is gaining huge momentum to achieve ubiquitous wireless connectivity. Connected autonomous driving (CAV) is a critical vertical envisioned for 6G, holding great potentials of improving road safety, road and energy efficiency. However the stringent service requirements of CAV applications on reliability, latency and high speed communications will present big challenges to 6G networks. New channel access algorithms and intelligent control schemes for connected vehicles are needed for 6G supported CAV. In this paper, we investigated 6G supported cooperative driving, which is an advanced driving mode through information sharing and driving coordination. Firstly we quantify the delay upper bounds of 6G vehicle to vehicle (V2V) communications with hybrid communication and channel access technologies. A deep learning neural network is developed and trained for fast computation of the delay bounds in real time operations. Then, an intelligent strategy is designed to control the inter-vehicle distance for cooperative autonomous driving. Furthermore, we propose a Markov Chain based algorithm to predict the parameters of the system states, and also a safe distance mapping method to enable smooth vehicular speed changes. The proposed algorithms are implemented in the AirSim autonomous driving platform. Simulation results show that the proposed algorithms are effective and robust with safe and stable cooperative autonomous driving, which greatly improve the road safety, capacity and efficiency.