Urban infrastructure is vital for sustainable cities. In recent years, municipal governments have invested heavily in the expansion of bike lane networks to meet growing demand, promote ridership, and reduce emissions. However, reallocating road capacity to cycling is often contentious because of the risk of amplifying traffic congestion. In this paper, we develop a method for planning bike lanes that accounts for ridership and congestion effects. We first present a procedure for estimating parameters of a traffic equilibrium model, which combines an inverse optimization method for predicting driving times with an instrumental variables method for estimating a commuter mode choice model. We then formulate a prescriptive model that selects paths in a road network for bike lane installation while endogenizing cycling demand and driving travel times. We conduct an empirical study on the City of Chicago that brings together several data sets that describe the urban environment—including the road and bike lane networks, vehicle flows, commuter mode choices, bike share trips, driving and cycling routes, demographic features, and points of interest—with the goal of estimating the impact of expanding Chicago’s bike lane network. We estimate that adding 25 miles of bike lanes as prescribed by our model can lift cycling ridership from 3.6% to 6.1%, with at most a 9.4% increase in driving times. We also find that three intuitive heuristics for bike lane planning can lead to lower ridership and worse congestion outcomes, highlighting the value of a holistic and data-driven approach to urban infrastructure planning.