Wireless broadcast routing is a complex problem, shown in the literature to be NP-complete. Current protocols implement either heuristics to find solutions that are not guaranteed to be optimal or classic flooding. However, many future use cases, like automotive applications, industrial robotics, and multimedia broadcast, will require efficient yet reliable methods. In this work, we use contextual multi-armed bandits together with opportunistic routing (OR) and network coding (NC) to find approximately optimal solutions to the problem of broadcast routing in a distributed fashion. Each router independently learns its own transmission credit, i.e., the number of packets to forward for each innovative packet received, so that the airtime cost, subject to latency constraints, is minimized. Results show that the proposed solutions, particularly the deep learning based one, vastly improve the overall reliability, while performing close to MORE multicast in terms of airtime and to B.A.T.M.A.N. in latency, both being the best candidates in the respective discipline among the tested ones.