This answer explores the theoretical cost differences between building equivalent roads and bike lanes. It does not put any dollars on the costs as these include much more than the road / bike lane itself (rails, markings, signs, lights, noise protection, etc.) that depend heavily on the exact location.
First, we need to ensure that the bike lane and the motorway are actually comparable. I'll take the throughput for this, the count of vehicles passing any point within a given time span:
Assume that cars drive 100 km/h and keep a safety distance of 30m. With the length of a car (5m), we get a rate of
100000/35 = 2900 cars per hour.
Assume that bikes drive 20 km/h and keep a safety distance of 6m. With the length of a bike (2m), we get a rate of
20000/8 = 2500 bikes per hour.
Ok, so a single lane of 100 km/h motorway has about the same throughput as a single lane of bike path. However, bikes are not as wide as cars, and that is one point where you can get significant cost reductions: A 100 km/h road needs to allocate at least 3.5m width per lane (2.5m truck plus safety distances), a cycle path may get away with 1.5m (0.5m bike plus safety distances). I.e. the road consumes about twice the space that the bike lane consumes.
Another factor is the robustness of the road. I cannot give numbers on this, but 2t cars to 40t trucks at 100 km/h put a lot more stress on the road than 100kg cyclists do. The asphalt of the motorway needs to be much thicker and well-constructed than the bike lane to last the same amount of years/vehicles. However, road construction vehicles are heavy as well, and the bike lane needs to survive its own construction. As such, there is a lower limit on the robustness of a bike lane that has nothing to do with the traffic it's intended for. Nevertheless, you need significantly less material to construct 1 m^2 of bike path than you need for the same area of motorway.