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Submodular optimization, particularly under cardinality or cost constraints, has received considerable attention, stemming from its breadth of application, ranging from sensor placement to targeted marketing. However, the constraints faced in many real domains are more complex. We investigate an important and very general class of problems of maximizing a submodular function subject to general cost constraints, especially focusing on costs coming from route planning. Canoni- cal problems that motivate our framework include mobile robotic sensing, and door-to-door marketing. We propose a generalized cost-benefit (GCB) greedy al- gorithm for our problem, and prove bi-criterion approximation guarantees under significantly weaker assumptions than those in related literature. Experimental evaluation on realistic mobile sensing and door-to-door marketing problems, as well as using simulated networks, show that our algorithm achieves significantly higher utility than state-of-the-art alternatives, and has either lower or competitive running time.