This paper investigates the feasibility of a resource prefetcher able to predict future requests made by web robots, which are software programs rapidly overtaking human users as the dominant source of web server traffic. Such a prefetcher is a crucial first line of defense for web caches and content management systems that must service many requests while maintaining good performance. Our prefetcher marries a deep recurrent neural network with a Bayesian network to combine prior global data with local data about specific robots. Experiments with traffic logs from web servers across two universities demonstrate improved predictions over a traditional dependency graph approach. Finally, preliminary evaluation of a hypothetical caching system that incorporates our prefetching scheme is discussed.