You can meet Guardian BunBun at the Dream Carnival of HKO, where he is available as one of three guardians for the Dream Carnival you may choose from. This escort-character will explain the different areas of the Dream Carnival as soon as you get close to them and will introduce a few important characters of Sanrio Land.
After you have chosen your guardian, he will always stay close to you just like a pet would. But you won't need to feed, pet or clean him. He also won't carry anything for you like some pets do and doesn't have any pet-stats. He neither will fight with/for your nor help you collect materials.
When you leave the Dream Carnival going to Sanrio Harbour the guardian will stay behind to help another newcomer.