Prerequisites: Max out Bubble's level 1 friendship
Reward: 150 G
Unlocks: Bubble level 2 friendship, Seed Collections
Unlocking Bubble's first friendship quest requires that you max out her initial friendship meter with you. This is fairly simple, as Bubble almost always hangs out at the same two spots. If she's not at Forrest's House, to the south of Moonbury Town, she'll be at the Ranger Post, just north of the house. Forrest is usually here, too, so you can kill two birds with one stone.
Boost Bubble's friendship with you and she'll post a notice on Moonbury's Bulletin Boards, asking for your help. Go to Forrest's House between 8:00 and 17:00, Monday to Sunday, to trigger the cut scene. She'll point you towards her rabbit, Cotton, who is apparently sick.
You'll suggest that Bubble isn't feeding Cotton the proper food, and Bubble will go off to find a different food source. The quest will end, and you'll gain a tiny reward, along with a boost to level 2 of your relationship with Bubble. You'll also unlock the quest Seed Collections on the other side of this new level of friendship. Yep, it's just that simple.