If you have wireless hotspot capability it is as simple as turning on mobile hotspot, noting the ssid (the name you gave your hotspot) and the password, then on your xbox go to: Settings, System, Network Settings.
UPDATE 1/5/15 9.15am Microsoft is rolling out a new Xbox 360 firmware update that adds USB hard drive support up to 2TB.
Pretty painless all in all..right back to not having the system connected after if you like and only connect when a new update is out.
Check with your service provider, but you might be able to make your phone a mobile hotspot, then connect your xbox wirelessly (via wifi) to that.
I followed the instructions, so I didn't know why I got an "unreadable disc" error.
Updates are usually downloaded automatically when one is available.
If your Xbox 360 is not connected to the internet, and you don't have a way to get it online, you can download updates from the various fan communities and apply them manually.
It would be much easier to carry your console over to a friend's house and briefly barrow their internet connection to update your version of Minecraft.
Your phone will have to have a wireless hotspot service enabled in order for that to work.