Alpine Road by motorcycle?

Is it possible to do Alpine Road with your own mean of transport (motorbike) ? Or the only way to do it is using the public busses, cable cars etc?

Are you talking about the Tateyama Kurobe Alpine Route?
If you are, unfortunately no.
https://www.alpen-route.com/en/

You can only go halfway of half.
https://www.alpen-route.com/en/transport_new/overview.html
The route map in "wiki" will be easier to understand than above on the official website.
https://en.wikipedia.org/wiki/Tateyama_Kurobe_Alpine_Route

Read FAQ and more.
https://www.alpen-route.com/en/information/faq.html

Or, you may be misunderstanding
"Japan Romantic Roads(Romantische Straße)" btw Ueda, Nagano and Nikko, Tochigi.
https://www.jrs-roman.org/

Also you never heard their forum?
http://www.gaijinriders.com/forum.php

And if you can read Japanese well, you should buy these most famous touring guides.
http://www.mapple.co.jp/mapple/product/map/drive/touringmapple.html
Many touring riders still thinking, this is "the Bible".
https://goo.gl/stqJsz
But recently, riders(even car drivers and cyclists) using smartphone with Navi apps is increasing.
https://goo.gl/wTP6an

Thank you very much for all suggestions :) I'll be riding around Japan with my motorbike and I'm looking forward this trip. Thank you!