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Cycling is a crucial part of sustainable urban transportation. Promoting cycling critically relies on a sufficiently developed bicycle infrastructure. However, designing efficient bike path networks constitutes a complex problem that requires balancing multiple constraints while still supporting all cycling demand. Here, we propose a framework to create families of efficient bike path networks by explicitly taking into account the demand distribution and cyclists' route choices based on safety preferences. By reversing the network formation process and iteratively removing bike paths from an initially complete bike path network and continually updating cyclists' route choices, we create a sequence of networks that is always adapted to the current cycling demand. We illustrate the applicability of this demand-driven planning scheme for two cities. A comparison of the resulting bike path networks with those created for homogenized demand enables us to quantify the importance of the demand distribution for network planning. The proposed framework may thus enable quantitative evaluation of the structure of current and planned bike path networks and support the demand-driven design of efficient infrastructures.