Do they only bike in the rural parts?

Yes, mostly. At least in the rural parts where I visited, the bike path is the norm and everyone is using it.

places that are much further from the bigger cities where the actual jobs are.

Then you move closer to your job. Communing form whatever remote farm to a city every day for work is absolutely not normal. Living close to work is what most of the people do (by definition), and it works for most of the people. Worst case scenario you move to a town-satellite that is connected to a big city via rail network. If fucking Russia figured it out, Denmark can do it too, it's not a rocket science. Farm workers who work on their farms and live their isolated lives still will have to use cars, but first of all they're in a minority, even in agrarian developed countries it's like 1% of population give or take. For everyone else cars is not a necessity and the best and only option, and if it is, it's a failure of infrastructure and needs to be fixed first priority.