For bugs you simply rerelease the game - put the new content in your game, put it through peer review again and the magic of Xbox does the rest.
Current players will get the 'This title has an upgrade' dialog and it will auto patch
New people will simply get the new version.
Note that XBLIG do not get the option to make the upgrade mandatory - so for whatever reason some people could stay on an old version. This is really only relevant if you have a network game where you need to be concerned about new and old versions meeting.
There is no DLC for XBLIG. That's reserved for XBLA titles so you need a publishing contract.