If you were going to bring just one thing on a massively long, tri-state bike ride, what would it be? A bottle of water? A map? Adam carries a package with him. It's all wrapped up, so we don't know what's inside, but he says it's a gift for his father.
The package comes up several times throughout the book: Adam packs it when he leaves, mentions how it gets wet in the rain (which doesn't bother him), and several times he reaches out to touch it and hold it tight, for fear of losing it. For example, when he runs into Whipper and the other bullies, he thinks:
The package is for my father and nobody, nobody is going to take it away from me or prevent me from bringing it to him. I stand there like a tree. I will not bend. I will not give him the package. I am the package. (14.38)
Just like he is the bike, Adam also is the package (not to mention the cheese). So the package means a lot to Adam. Why does he associate himself with so many inanimate objects?
We find out at the end what's inside the package: Pokey the Pig, his old stuffed animal and "friend" (2.2). We remember Pokey from the beginning of the book when Adam held him while listening to his parents happily whispering in the other room. At the end of the book, when he's holding Pokey in his arms at the hospital, Adam seems to have almost reverted back to this time from his childhood. Unlike all the other memories and details from Adam's past, which have been so hard for him to retain, Pokey is an object from the past that he can physically hold on to. Perhaps the reason Adam worked so hard to protect that package on his bike ride is because inside it was his only connection to the past.