Did some further research on this issue.
Seems that OTP is only supported at a Premium plan. That's why I couldn't get it to work. The Mac Client does not mention anything and just generates a random (not 6 digits) code. Which is not accepted when setting up two factor authentication in October CMS.
I found out by using the web client of Bitwarden that you need a Premium plan for it to work.
So I'm pretty sure it will work with our plugin when I read this:
The Bitwarden Authenticator is an alternative solution to dedicated authentication apps like Authy, which you can use to verify your identity for websites and apps that use Two-step Login. The Bitwarden Authenticator generates 6-digit Time-based One-time Passwords (TOTPs) using SHA-1 and rotates them every 30 seconds.
Our plugin uses the default algorithm (SHA1) and generates a TOTP.
Please let me know your findings, because I cannot test it properly without having a Premium plan for Bitwarden.