One method of dealing with a potentially endogenous variable (a right hand side regressor that doesn't meet the orthogonality condition - like bike lanes in a biking regression) is to find some other source of variation that is correlated with the potentially endogenous variable (bike lanes) but uncorrelated with the unexplained variation in the dependent variable (bike riders). That data is then used to 'instrument' the potentially endogenous variable - basically to use this new source of 'clean' variation to identify the true causal effect.
In the bike lane example we would need something that is correlated with the amount of bike lanes but uncorrelated with the unexplained variation in biking. I can't think of anything good but you might. FOr example, suppose some cities have bike lobbies that successfully get more bike lanes - well the presence of, and political power of, these lobbies is probably a function of the number of bike riders so it doesn't work as an instrument.
Another method is to find a natural experiment. These are usually not as natural as we would like but the approach is probably more promising in this case - find some exogenous change in bike lanes (a sudden expansion of lane provision due to some unexpected surplus budget in the dept. of transport, for example) and see if such a sudden increase in bike lanes leads to a sudden increase in bikers.
Anyway, my point below is that it seems pretty obvious that bike lanes will lead to more biking, but it is devilishly hard to show it convincingly in the data.
You may ask, if it is so obvious, why do we need to show it statistically? Well, it is important because there will always be questions about how much money to devote to bike infrastructure. The answer to this question relies critically on the biking response to bike infrastructure. If your goal is to increase biking you need to know by how much riding increases with new bike lane miles. In econo-speak, you need to know the bike lane mile elasticity of bike ridership.
So send your good ideas along and if any seem promising, we'll see about testing them.