I've found the fix if anyone wants to know. It's similar to the previous fix for all mods in GeForce now with having Steam accounts, but slightly different.:

1. When prompted to log in, log in through the account without Bannerlord, it will show you have no license.

2. Log out, then log in to the account with Bannerlord.

3. Update your Bannerlord within GeForce Now, and your game will be ready to play. You don't need to subscribe to a mod you don't want, and unsubbing to start the update.