While writing out a more detailed description of the behavior, I stumbled upon the solution myself.
When you try to install the game over the internet, just let it start, and then cancel it. This will both remove the installation and download from the queue, but apparently also remove the knowledge of the installation from the Xbox One.
So:
- Start the online install
- Cancel it
- Return to the home screen
- Notice that the disc tile has now changed to "Install disc"
- Activate the disc tile to start the installation from the disc.
This worked, the game now installs from the disc. Obviously any downloaded DLC's will still need to be downloaded, but for the purpose of this question this is not relevant.
Now, what do you do when you get back home and want to plug in the external drive?
Here's what I did. I first uninstalled the game using the storage management.
This makes my Xbox One forget that I had the game installed. Make sure you don't delete any savegames you have on the console.
Then, you turn off the Xbox One, plug in the external drive, and turn it back on.
Once you do that, the disc tile still says "Install disc". Ignore that. Instead either use your pinned link to the game, the tile for the game (if it shows up on the home screen), or navigate to your games and apps list and activate it. You should get a message saying not to unplug the external drive, and that your game will be ready soon.
A few seconds later you can try again and the game should now start.
There are all kinds of servers that you can join via your Minecraft client on your X360. Check out some of the posts here. You and your friend would need to join the same multiplayer server simultaneously to hang out together.
http://www.minecraftforum.net/forums/minecraft-xbox-360-edition/mcx360-multiplayer/mcx360-servers
If you're looking to just start a local, split-screen type of multiplayer game, you'd need to have an HD screen (something displaying in full HD, 1920x1080 AKA 1080p), grab a second controller and have your second player sign in while a local world is running. Voila!
Best Answer
You need to log in and enter the game at least once before you can play it offline.
(Added as an answer for posterity)