  Bicycle infrastructure networks must meet the needs of cyclists to position
cycling as a viable transportation choice in cities. In particular, protected
infrastructure should be planned cohesively for the whole city and spacious
enough to accommodate all cyclists safely and prevent cyclist congestion -- a
common problem in cycling cities like Copenhagen. Here, we devise an adaptive
method for optimal bicycle network design and for evaluating congestion
criticalities on bicycle paths. The method goes beyond static network measures,
using computationally efficient adaptation rules inspired by Optimal Transport
on the dynamically updating multilayer network of roads and protected bicycle
lanes. Street capacities and cyclist flows reciprocally control each other to
optimally accommodate cyclists on streets with one control parameter that
dictates the preference of bicycle infrastructure over roads. Applying our
method to Copenhagen confirms that the city's bicycle network is generally
well-developed. However, we are able to identify the network's bottlenecks, and
we find, at a finer scale, disparities in network accessibility and
criticalities between different neighborhoods. Our model and results are
generalizable beyond this particular case study to serve as a scalable and
versatile tool for aiding urban planners in designing cycling-friendly cities.
