i am going by motorbike
That would need a destination, like "I am going to Paris by motorbike".
Why does this not work? eg. "how are you getting there?" "I am going by motorbike"
OK, you've got some point. Added now.
Can I say "jadę motorem"? If so, what is the difference between these two?
You can. I think they're the same, but maaaaybe "Jadę motorem" has more chance of "I am just a passenger" than "Jadę na motorze" does.
Co się stało, Waldku? Czy twoja odpowiedź nie została przyjęta?
I am going on a motorbike?
Yes, it works.