I've found an inexpensive way of backing up your Minecraft world. For this method you will need:

• My Files Explorer installed on your Xbox (available in a 24 hour trial or for >$3),
• An external storage device,
• The account of which created/owns the world

The Steps

• Connect your external storage device, and wait until it is ready,
• Sign into the account of which created/owns the world you are trying to backup,
• Open up My Files Explorer with the above account,

If you can't see the filenames, press the button that shows 3 dots, press Settings, then choose the bottom left choice for themes or any others that show filenames.

• Go to Isolated Storage
• Press the Local button at the top center of your screen,
• Open Packages/Microsoft.MinecraftUWP.../LocalState/games/com.mojang/minecraftWorlds
• Now find the world folder that you want to backup

The world names are going to look like gibberish, you can each folder until you find the one that has the name of your world in levelname.txt and/or the world_icon.jpeg picture is the right picture.

• Then press the pause button(the button that has 3 lines on it) and select Copy Folder
• On the right of your screen should be a menu that has a button called This Device press it.
• Go into Removable Devices/(your external storage device) and press the pause button then hit Paste

Once it is done pasting, you can then close the app, shutdown, and take out your drive.