Final answer:
The 'I' in the sentence is Bilbo Baggins. He is reflecting on what his father, Bungo Baggins, would have thought of his actions, which is a common theme for Bilbo's character in J.R.R. Tolkien's works.
Step-by-step explanation:
The sentence "What his father Bungo would have thought of his, I daren't think." refers to Bilbo as the 'I' in the sentence. This can be inferred from the context of J.R.R. Tolkien's book, where Bilbo Baggins often reflects on what his late father, Bungo Baggins, would have thought about his adventures. Since the text provided does not contain any reference to this specific sentence, we rely on the well-known character relationships in Tolkien's literature to determine that Bilbo is speaking about his father Bungo here. It is not likely that the characters Gandalf or Dwalin would refer to Bungo as a father, thereby the most logical answer is that Bilbo is the one contemplating his father's opinion.