There aren't technically three "Introductions." There is one "Introduction," one "Notes to Introduction," and one "Textual Note." The last two are, as is evident from their titles, very different from an "Introduction."
The Introduction gives a social biography of David Hume from Bell's perspective with quotes and anecdotal stories from such notable personalities as James Boswell, most famous for his biography on his close friend, Doctor Samuel Johnson.
Boswell records that Hume told him that the morality of every religion was bad and that 'when he heard a man was religious, he concluded he was a rascal, though he had known some instances of very good men being religious.' Boswell was convinced ... [that Hume] persisted in disbelieving a future state even when he had death before his eyes.'" (Introduction)
"Notes to Introduction" and "Textual Notes" provide expansions on, additions to, explanations of the information Bell gives and the choices he makes. For instance in "Textual Notes," Bell explains that his version is based on Hume's original manuscript though with "some modernizations."
"Best" in reference to translations or to edited versions of earlier manuscripts is not an absolute value: texts labeled "best" have many dissenters to that categorization. As a rule of thumb, "best" is contemporarily awarded to edited or translated texts based upon (1) modernization and (2) linguistic or stylistic simplification.
An illustration of this is that contemporary editions of Homer's Iliad are considered "best" when they ignore replicating Homer's meter and rhyme or when they render the Iliad in prose form instead of poetic stanza. These editorial and translation choices are thought "best" because they seem to make the text more "accessible" to modern readers.
It stands to reason, then, that at least one probable reason Martin Bell's edition of Hume's Dialogues is "best" is because of the modernization of language he opts for. Perhaps another is that Bell is a highly accomplished and prestigious Hume scholar and academic.