So the first draft was initially going to begin with "When M----", but this idea was immediately dropped in favor of:
When Bilbo, son of Bungo of the family of Baggins, had celebrated prepared to celebrate his seventieth birthday there was for a day or two some talk in the neighborhood.
The second draft begins:
It is clear that Tolkien's originaloriginal intent was to begin the story by mentioning Bilbo1 and his impending birthday party. He began to write "When Mr. Bilbo Baggins...", but for whatever reason, changed his mind and dropped the "Mr.", opting instead for "When Bilbo". I haven't read much more than this part of The Return of the Shadow yet, but skimming through the rest of the book, it appears that the version of the first chapter that was eventually published in the finished book was at least the fifth or sixth revision.
1 The third draft deviated from the prior pattern. Instead of beginning with "When [Mr.] Bilbo Baggins and his stupid birthday blah blah blah", it began by mentioning Bilbo's son:
When Bingo, son of Bilbo, of the well-known Baggins family, prepared to celebrate his fifty-fifth seventy-second birthday there was some talk in the neighborhood, and people polished up their memories.
- The History of Middle-earth, Volume VI, The Return of the Shadow, Chapter I: A Long-Expected Party, p. 28
This change reflects Tolkien's wavering on the question of whom the story would be about - at first, it seems, the part we know as Frodo's was going to be filled by Bilbo himself. At some point as he was writing, Tolkien scrapped this idea and decided to make Bilbo's son Bingo the main character. This idea also shows up (albeit in a further revised form) in the fourth draft:
In the first sentence of the chapter, 'Bingo, son of Bilbo' was altered to 'Bingo Bolger-Baggins'; and in the third sentence 'Bingo's father' was altered to 'Bingo's uncle (and guardian), Bilbo Baggins'.
This version of the chapter is the first to describe the relationship between Bilbo and the main character of the story in the way with which we are familiar: although the main character's name is still unfamiliar to us, he is now Bilbo's nephew and ward, not his son. This nephew, Bingo, would not become "Frodo" until a much later stage in the writing process.