Millimeter wave (mmWave) communication has emerged as a propelling technology in vehicular communication. Usually, an appropriate decision on user association requires timely channel information between vehicles and base stations (BSs), which is challenging given a fast-fading mmWave vehicular channel. In this paper, relying solely on learning transmission rate, we propose a low-complexity semi-distributed contextual correlated upper confidence bound (SD-CC-UCB) algorithm to establish an up-to-date user association without explicit measurement of channel state information (CSI). Under a contextual multi-arm bandits framework, SD-CC-UCB learns and predicts the transmission rate given the location and velocity of the vehicle, which can adequately capture the intricate channel condition for a prompt decision on user association. Further, SD-CC-UCB efficiently identifies the set of candidate BSs which probably support supreme transmission rate by leveraging the correlated distributions of transmission rates on different locations. To further refine the learning transmission rate over the link to candidate BSs, each vehicle deploys the Thompson Sampling algorithm by taking the interference among vehicles and handover overhead into consideration. Numerical results show that our proposed algorithm achieves the network throughput within 100%-103% of a benchmark algorithm which requires perfect instantaneous CSI, demonstrating the effectiveness of SD-CC-UCB in vehicular communications.