This study of 90 large American cities shows that cities with a greater supply of bike paths and lanes (both on- and off-street) have significantly higher bike commute rates, even when controlling for land use, climate, socioeconomic factors, gasoline prices, public transport supply, and cycling safety.
Buehler, Ralph, and John Pucher. (2012). Cycling to work in 90 large American cities: new evidence on the role of bike paths and lanes. Transportation. 39(2), 409-432.