Where can I find my challenges for Cosmetics which include a challenge bundle in Fortnite?

When you first navigate to the Quest Tab, it will auto-select the game mode you are in, showing quests for it. 

To see all quests for all game modes, including the Challenges from purchased cosmetic bundles, check the step below:

1.  Go to the Quests tab and:
   • On PC, press the ESC key.
   • On Xbox, press the B button on the controller.
   • On PlayStation, press the O button on the controller.
   • On Nintendo Switch, press the A button on the Joy-Con controller.

This will go back to the main view, where the Miscellaneous tab will be listed on the left, and any Challenges from cosmetic purchases can be found there.