Lord of the Rings Geek

Yup. That's me.

Question: when all the elves left Rivendell and went to the undying lands (except Lord Elrond, Arwen, and some random extras), where was Bilbo? Initially, he left the Shire to retire in Rivendell, he's not in The Two Towers at all, but then reappears at the end of Return of the King to leave with Gandalf and Frodo on the Gray Ships. My questions is...where was Bilbo during the war for middle earth??? I know he's old and can't fight, but why didn't he leave earlier on the ships??