You need to have xbox live so you can download updates. So sign in with an account that has xbox live and start up minecraft with the disc. It should prompt you to update your game (TU13).
Note, however, that as your post is worded, updates can't be downloaded to the disk itself. The disk will always stay the same- the updates are just downloaded to your HD and then applied whenever (and each time) you start the game.
EDIT: Wait.... do you actually mean "the disk" (meaning the retail MC disk, in that case see above), or to "a disk" (meaning copying the updated version to your own CD)?
EDIT: Wait.... do you actually mean "the disk" (meaning the retail MC disk, in that case see above), or to "a disk" (meaning copying the updated version to your own CD)?