The Red Book Of Westmarch

Alright, for those of you who've read the prologue, this has been really bothering me. Bilbo contributed to the red book correct? A lot if I remember correctly. And "There and back again" is part of the red book. Frodo also contributed. But this quote has been really bothering me, it's straight from the prologue.

"[The Red book of westmarch is the] most important source for the history of the war of the ring was so called because it was long preserved at Undertowers, the home of fairbairns, wardens of the westmarch. It was in origin Bilbo's private diary, which he took with him to rivendell. Frodo brought it back to the shire, together with many loose leaves of notes. And durring S.R. 1420- I he nearly filled it's pages with his account of the war. But annexed it and preserved with it, probably in a single red case, were the three large volumes, bound in red leather, that bilbo gave him as a parting gift."

So... If frodo took Bilbo's diary... and made the Red Book from that... what did bilbo give frodo as a parting gift? I'm so confused.