I just finished the main quest in Borderlands 2 and have the season pass downloaded. The DLC are added to the fast travel station, but there is a star by all of the names. For example, "*Unassuming Docks". Whenever I click on these it brings up an XBox screen saying I've already purchased this item and have downloaded it before, it then asks me to download it again. I'm not sure how to actually PLAY the DLC though. The searching I've done indicated it should work after I finish the main quest. I'm a level 30 mechromancer if it makes any difference.
In case this is just a quick fix and I am understanding you correctly, you will need to actually download the DLC separately. The season pass just lets you download the DLC for "free" (for lack of a better word).
If it's a problem beyond this, I would verify that the DLC is actually downloaded. From the Settings tab go System > Storage > Hard Drive > Games and Apps > Borderlands 2. From there you can see what is actually downloaded for Borderlands 2. To play the DLC, each individual piece of content that you wish to play will need to be downloaded. Each one will be titled accordingly. If you don't see the DLC you want to play on that list, you will need to load up Borderlands 2 and go to the store and download them from there.
If the DLC is listed as being on your Hard Drive and the game still won't let you access it (through the Fast Travel Station), then the only thing I can recommend is removing it from your Hard Drive and re-installing it.
Hope this helps - no one should be denied their Borderlands! :D