Unfortunately we don't have any experience using OnlyOffice with ownCloud, hopefully someone in the Bitnami community has.
It seems that OnlyOffice depends on a few services being available, the only conflicting one being Nginx (Bitnami OwnCloud uses Apache).
In order to avoid port issues, you could try to follow this guide to configuring it using Docker instead: http://www.onlyoffice.com/blog/2015/02/how-to-install-onlyoffice-in-just-a-few-minutes-using-docker-service/
But please keep in mind you should use different ports, as Apache is already using ports 80 and 443, e.g. with the following parameters:
-p 81:80 -p 444:443
After alternative could be starting a new Google Cloud instance only running OnlyOffice, where you would need to follow this guide instead: https://helpcenter.onlyoffice.com/server/linux/document/linux-installation.aspx
For security purposes, you should limit via firewall the access to that instance's 80 and 443 port, only from your original instance's IP.
I hope it helps!