This paper presents an incremental formal development of the Dynamic Source Routing (DSR) protocol in Event-B. DSR is a reactive routing protocol, which finds a route for a destination on demand, whenever communication is needed. Route discovery is an important task of any routing algorithm and formal specification of it, itself is a challenging problem. The specification is performed in a stepwise manner composing more advanced routing components between the abstract specification and topology. It is verified through a series of refinements. The specification includes safety properties as set of invariants, and liveness properties that characterize when the system reaches stable states. We establish these properties by proof of invariants, event refinement and deadlock freedom. The consequence of this incremental approach helps to achieve a high degree of automatic proof. Our approach can be useful for formalizing and developing other kinds of reactive routing protocols (i.e. AODV etc.).