[Child of the 7th Age]

I think Frodo was 12 when his parents died. He wasn't adopted by Bilbo till age 21. Between 12 and 21, he grew up in Brandy Hall in Buckland. There were apparently a whole parcel of relatives living there together so Frodo would have had plenty of company.

It doesn't sound like anyone in particular was keeping an eye on him, so he could kind of run wild (and get in trouble stealing mushroom from Farmer Maggot!).

I imagine that Bilbo paid frequent visits to his relatives, and Frodo must have really hit it off with him. I can even imagine Bilbo chatting with Gandalf when he came to the Shire and talking with him about his plans to adopt Frodo.

How Lobelia Sackville-Baggins must have fussed about that adoption as she probably realized it could cut her out of the inheritance of Bag End.

Sometimes we forget how important Bilbo was to Frodo, since we really don't see much of them together in LotR. But Tolkien clearly stated that Bilbo was Frodo's favorite person in the whole world (by implication, that meant even more than Sam which is hard to believe!) So even though Frodo must have missed Sam very much when he sailed West, he did have the consolation of being near Bilbo again.