The Chasing Shauna quest involves Shauna, Bart and Milhouse. However, it’s important to know that buying Shauna and starting her quest doesn’t unlock either Bart or Milhouse. Chasing Shauna will only run if you have already unlocked both characters in your main game.

So, even if you’re getting a message to build the van Houten House or Bart’s treehouse as part of Shauna’s quest, neither event will happen unless you’ve completed all the tasks in order in the main game. And that’s because a premium character is designed to add to the game, rather than speed it up. A premium character never unlocks characters or buildings ahead of schedule.

There’s a walkthrough of the Chasing Shauna quest here and a good walkthrough of the entire game in the official game forums here. At least it will let you know how many steps there are between you, Bart, and getting started on Chasing Shauna.