Who are Bilbo's ancesters?

Bilbo's ancestors were the Bagginses and the Tooks.

This hobbit was a very well-to-do hobbit, and his name was Baggins. The Bagginses had lived in the neighbourhood of The Hill for time out of mind, and people considered them very respectable, not only because most of them were rich, but also because they never had any adventures or did anything unexpected: you could tell what a Baggins would say on any question without the bother of asking him. This is a story of how a Baggins had an adventure, found himself doing and saying things altogether unexpected. He may have lost the neighbours' respect, but he gained-well, you will see whether he gained anything in the end.

The mother of our particular hobbit … what is a hobbit? I suppose hobbits need some description nowadays, since they have become rare and shy of the Big People, as they call us. They are (or were) a little people, about half our height, and smaller than the bearded Dwarves. Hobbits have no beards. There is little or no magic about them, except the ordinary everyday sort which helps them to disappear quietly and quickly when large stupid folk like you and me come blundering along, making a noise like elephants which they can hear a mile off. They are inclined to be at in the stomach; they dress in bright colours (chiefly green and yellow); wear no shoes, because their feet grow natural leathery soles and thick warm brown hair like the stuff on their heads (which is curly); have long clever brown fingers, good-natured faces, and laugh deep fruity laughs (especially after dinner, which they have twice a day when they can get it). Now you know enough to go on with. As I was saying, the mother of this hobbit - of Bilbo Baggins, that is - was the fabulous Belladonna Took, one of the three remarkable daughters of the Old Took, head of the hobbits who lived across The Water, the small river that ran at the foot of The Hill. It was often said (in other families) that long ago one of the Took ancestors must have taken a fairy wife. That was, of course, absurd, but certainly there was still something not entirely hobbit-like about them, - and once in a while members of the Took-clan would go and have adventures. They discreetly disappeared, and the family hushed it up; but the fact remained that the Tooks were not as respectable as the Bagginses, though they were undoubtedly richer. Not that Belladonna Took ever had any adventures after she became Mrs. Bungo Baggins. Bungo, that was Bilbo's father, built the most luxurious hobbit-hole for her (and partly with her money) that was to be found either under The Hill or over The Hill or across The Water, and there they remained to the end of their days. Still it is probable that Bilbo, her only son, although he looked and behaved exactly like a second edition of his solid and comfortable father, got something a bit queer in his makeup from the Took side, something that only waited for a chance to come out. The chance never arrived, until Bilbo Baggins was grown up, being about fifty years old or so, and living in the beautiful hobbit-hole built by his father, which I have just described for you, until he had in fact apparently settled down immovably.