There's also a causal effect from biking to showering, although there are a few other things in the causal path such as getting sweaty. If you walked home instead of biking, you might avoid the shower. So biking does cause you take a shower.
That's the key to it IMHO. There has to be isolation for identifying causal relationships. Science is the work to be sure you're measuring the thinnest partial derivative.
I'd generalize it to "All else being equal"
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On another note, I believe there are classes in causality, arranged in a hierarchy. If you're studying the 'physical' class (level 0), you'll end up with causators in the same level or higher ('system' class, level 1).
In our case the 'all things being equal' has to take account of an instance of a higher class (the human 'system' regulating the fuel input with the pedal)
The level 2 would be system of systems; for example processes like the Darwinian evolution.
If all we mean by 'x causes y' is that 'y is a function of (perhaps among other things) x', then.. fine?
'causal path' refers to a path in a directed acyclic graph that models the causality. https://cran.r-project.org/web/packages/ggdag/vignettes/intr... has some examples.