This is skipping a few years ahead. Close to the time that Bilbo adopts Frodo.
*~*~*~*~*~*~*~*
Dear Frodo.

My dear nephew, how is everything? Your birthday is quickly approaching, as is mine. My, I am just getting older, and you are becoming a fine young hobbit.

Sam wished for me to tell you hello, and that he hopes you shall come down soon. The little fellow certainly seems to look up to you as an older brother, and I know you think of him as a little brother. His sisters also wish to know when you are coming back down. I think you are becoming quiet a lady catcher, my dear boy!

Remember the matter that we discussed a while ago? Well, dear boy, I have discussed it with Saradoc, and he has agreed. At the party, I shall announce you as my heir and that you shall be moving in with me. But we shall keep that between the three of us for now. I shall see you then.

Your loving Uncle,
Bilbo