This chapter is, really, the first one in which Bilbo acts much like a burglar. He has, of course, the Ring to make him invisible, but he still has to creep around inside an elf-crowded underground palace without ever bumping into anyone or getting seen, and do so for days. I'm not clear on how long, exactly, but long enough that finding safe places to sleep must have been an occasional issue.
He also does a creditable job of investigating things, finding out where Thorin is and that there is a watery passageway out of the Elvenking's palace. I found it amusing to imagine Bilbo trying to lead a troop of whispering, cursing, bumbling dwarves through the mostly empty hallways between the prison cells and the barrel room. At times, the dwarves are a bit "Keystone cops".
The barrel-bound escape seems somewhat plausible, but equally plausible would have been, "and then when he opened the barrels at the end of things, half of the dwarves had drowned and were corpses, too stiff even to remove from their barrels, so they left them there for the men of Laketown to discover later". I have some sympathy for the dwarves' misgivings about the plan. However, while the dwarves are not great at planning or coordination, they do seem to be good at endurance and toughness, which is mostly what is required here.
Good choice on JRRT's part to simply state what the upshot was of the conversations which Bilbo overheard while riding barrels. If he had tried to give us the actual conversation, to the effect that the riverine pathway out of the forest was the only one left that was any good, it would either have taken forever, or sounded awfully unnatural, an "as you know, Bob".
Chapter 10