Multicast is the obvious choice for disseminating popular data on cellular networks. In spite of having better spectral efficiency than unicast, its performance is bounded by the user with the worst channel in the cell. To overcome this limitation, we propose to combine multicast with device-to-device (D2D) communications over an orthogonal channel. Such a strategy improves the efficiency of the dissemination process while saving resources at the base station. It is quite challenging, however, to decide which users should be served through multicast transmissions and which ones should receive the content via D2D communications. The progress of content dissemination through D2D communications depends on how users meet while on the move. The optimal decision for each content depends both on the status of the LTE channel (when the multicast transmission is executed) and on the evolution of the mobility process of the nodes from there on. We propose a learning solution based on a multi-armed bandit algorithm that dynamically selects the best allocation of users between multicast and D2D to guarantee the timely delivery of data. Numerical evaluations are performed to compare our proposal with the state-of-the-art scheme and an optimal but unfeasible strategy. We confirm that a proper mix of multicast and D2D helps operators save resources at the base station and that the learning algorithm can autonomously find a near-optimal configuration in a reasonable time.