Hi, welcome to the forum!
This might be helpful: https://musicbee.fandom.com/wiki/Importing
The Inbox is not a different folder, it's just a different conceptual section of the library, for holding things until they're ready for the main library. When you import files you can decide whether they should go to the inbox or the main library, whatever fits your process.
If you want to have a folder where new files are imported automatically, that's a monitored folder and you can set it up in Library Preferences.
For your use case, you might find it more helpful to install MusicBee Portable on the external drive so that you always have the application along with the audio files.