Hello Wojciech Cwajna
I have checked “bycyle-friendly” connections at Oebb:
In NJ 466 Vienna to Zurich are only three parking spaces for bycycles. It was not possible to book at ticketshop ÖBB. I found options for you from Vienna to Feldkirch
From Feldkirch to Erstfeld you will find connecting trains. In Interregio trains you need a ticket for also for your bycycle, and in Eurocity and IC SBB also a reservation for your bycycle.
Kind regards
Christoph