Here's an article about a study conducted in Sweden and Australia.

If only societal cost/benefits were considered, one kilometre by car cost €0.15 (AU$0.21), whereas society earned €0.16 (AU$0.22) for every kilometre cycled.

Those numbers appear very close, so to clear up any doubt: the car CBA was a net cost while cycling had a net benefit.

And even this is actually being very friendly to cars and unfriendly to cycling. Because even though most crashes between bikes and cars are caused by the car, the study counts this as a cost of cycling in its cost-benefit analysis. It also counts time as the biggest cost to cycling, which is fair in the abstract, but may miss two key details: (1) cycling for transport may reduce the time one needs to spend with dedicated exercise to keep healthy, so a 30 minute ride might only actually cost you 15 minutes, as an example. And (2) studies have noted that cyclists often take extra lengthy circuitous routes in order to stay safe and avoid cars—time would be lower if we had better biking infrastructure or if cars were used in a less unsafe manner.