Routing is one of the main drivers of the end-to-end performance of bundle transmissions over a disruption tolerant network given the potentially large impact of the temporary but long-term partitioning that can occur at different sections of the network. A neuromorphic networking approach that defines an adaptive bundle routing for disruption-tolerant networks (DTN) is proposed where spiking neuronal networks (SNN) are used to determine the routing decisions of autonomous agents. The event-driven information encoding of spiking neurons involves very low energy consumption, which makes this approach attractive for challenging DTN applications with limited access to energy sources. The SNNs are continually updated within an autonomic loop, which produces synapse strength updates that are proportional to the expected communication costs of the routing decisions. A reward shaping procedure and a delay-tolerant mechanism for finding the local link-state is proposed, which allows determining instantaneous learning rewards for the agents. The method was tested on an emulated space communications network with scheduled disruptions. The results show that the proposed cognitive routing approach offers improved bundle delivery performance under network congestion compared to the standard Contact Graph Routing.