Initially, Bilbo seems to be an extraordinarily self-centered hobbit, though this is not at all uncommon for members of his race. Hobbits largely keep to themselves and amuse themselves by spreading gossip about one another. Though Bilbo does do his best to provide for his guests, as this is considered a matter of utmost social priority for hobbits, the beginning of the book makes it quite clear that he resents those that won't keep to their own business, such as the dwarves, who greatly impose upon his hospitality. It seems dubious at this point that he would feel genuine compassion for any person without any sort of transaction in the relationship.

In the end of the story, however, it is quite clear that Bilbo has been moved to feel compassion for many of the people that he has met in his travels. Though the strife between the elves and dwarves has a long and contentious history, Bilbo, despite having traveled with the dwarves, feels a great deal of respect and admiration for the elves. Despite his friendship with Thorin, Bilbo chooses to give the Arkenstone to Bard and the elves. He does not do this to spite Thorin, but instead wants to give the elves and Bard some leverage so that they can reason with Thorin and avoid a continued standoff wherein all sides would be weakened.

In Chapter 9 of The Hobbit, Bilbo does show compassion toward the Wood-elves in one particular, small way. When he sneaks in to free the Dwarves from their cells, he manages to take the keys from the two Elven guards because they are drunk and asleep. Bilbo's plan is to release all the Ewarves, climb into empty wine barrels, and float down the river to freedom. Before he carries out step two and three of his plan, however, the text says that

Bilbo, before they went on, stole in and kindheartedly put the keys back on his [the guard's] belt.

Although this may seem like a somewhat inconsequential act, Bilbo's actions stem directly from his compassion for the Elven guard. Bilbo wants to save the guard from getting into too much trouble the following day when it is discovered that the prisoners are gone from their cells. Bilbo's act of re-locking the doors and returning the keys provides the guard with the argument that he truly does not know how they could have escaped⁠—he has his keys still, doesn't he?