The vehicular edge computing (VEC) system integrates the computing resources of vehicles, and provides computing services for other vehicles and pedestrians with task offloading. However, the vehicular task offloading environment is dynamic and uncertain, with fast varying network topologies, wireless channel states and computing workloads. These uncertainties bring extra challenges to task offloading. In this work, we consider the vehicle-vehicle offloading scenario, and propose a solution that enables vehicles to learn the offloading delay performance of their neighboring vehicles while offloading computation tasks. We design an adaptive learning-based task offloading (ALTO) algorithm based on the multi-armed bandit (MAB) theory, in order to minimize the average offloading delay. ALTO works in a distributed manner without requiring frequent state exchange, and is augmented with input-awareness and occurrence-awareness to adapt to the dynamic environment. The proposed algorithm is proved to have a bounded learning regret. Extensive simulations are carried out under both synthetic scenario and realistic highway scenario, and results illustrate that the proposed algorithm achieves low delay performance, and decreases the average delay up to 30% compared with the existing upper confidence bound based learning algorithm.