Bart is automatically unlocked with his treehouse - make sure to do all ! events - keep building houses - upgrade your stars as far as possible - eventually he'll pop up - it sometimes will matter if you do certain events before another - that it's delayed also note if a player is in a long quest (like 24 hours) that character may be needed for events to update so those on the tutorial try to keep free to get that event going
Actually from what I can tell stars have no bearing on quests as I'm getting the quest just fine and I took out every piece of fluff for now. Just have to have the character free for when it triggers and follow the quest chains until it unlocks, which can take a while when you have to build stuff to progress.
The stars do give a very slight bonus to xp and money earned though.