Headcanon: Bilbo eventually evolves into something of a Santa Claus figure to Hobbits.
“It became a fireside-story for young hobbits; and eventually Mad Baggins, who used to vanish with a bang and a flash and reappear with bags of jewels and gold, became a favourite character of legend and lived on long after all the true events were forgotten.”
Mad Baggins was remembered for randomly appearing with money, but Bilbo Baggins was well known for being extremely generous with his, especially to people who weren’t too well off. Frodo, of course, is just as free with his fortune as Bilbo was, as is Sam when he comes into it, and even Lobelia with what she has left after Saruman’s occupation, and as “Baggins” begins to decline as a name, it becomes somewhat synonymous with charity, and this gets mixed up in the legends about Bilbo’s funny adventures and ridiculous stories until everything’s too tied together to separate.
Bilbo would give out lots of gifts in the winter, to ensure everyone had warm clothes and a roof that didn’t leak, which is how he eventually became tied to Yuletide, and the legends start out as, “Mad Baggins will share his fortune with those who truly need it,” and eventually evolves into, “Good little Hobbitlings might get gifts from Mad Baggins,” and there are all sorts of pageantry and games, like someone will dress up as Mad Baggins and use Hobbit stealth magic and sleight of hand to “appear” in various places, set off a firecracker, and then run for it, and anyone who can catch him can have some candy out of his bag.
Long after Hobbits stop having dealings with Dwarves, and perhaps even after they stop believing in them altogether, they become mystical figures attached to the Mad Baggins legend, coming and going as they please and answering to nobody; anybody who catches a Dwarf may get cursed, but they also may win a treasure off of them like nothing else (and the curses, of course, are the sorts of dreadful things Hobbits can think of; thin foot-hair for a season, or never finding something until you’re looking for something else).
You know those creepy ornate woodland Santas, or like, the horrible Victorian illustrations? They have those too: Mad Baggins (a bright red nose and curly golden hair around his ears, bald on the top of his head and wearing boots of all things) accompanied by thirteen dwarves and a troop of ponies, passing out gifts and then disappearing with more than Hobbit skill. But the classic image of Mad Baggins, the one that springs to mind when children think of him, and appears in whatever their version of The Night Before Christmas is, garbs himself in green and silver and carries a sword (quite an outlandish thing among Hobbits!), and laughs often, being a great lover of song and good food and drink and practical jokes.
And if sometimes the perfect gift does appear out of thin air with no reasonable expectation, well. They say he learned from wizards too, and even though all things are diminished in the latter days, nobody ever said they were going to dwindle to nothing, did they? And it sits well with certain entities that at the end of the day, this is what’s left of a certain Dark Lord’s legacy; a legend borrowing the incidental property of his magic talisman to grant invisibility to bring gifts to children.