They wake up at the same time.

Bilbo is confused because the last thing he remembers is the gentle rocking of a wide boat on the wider sea; the cushions supporting his creaky, arthritic bones smelling strongly of rosemary and slightly of sea salt; the sounds of Gandalf puffing his pipe and of conversational ( edged just barely with anticipation ) Sindarin and of Frodo's warbling laughter melding pleasantly in his ear - but now he is curled up under his father's quilt, joints folded together without a singular complaint, gazing past his mother's curtains out to a sunbathed Shire.

Thorin is confused because he hadn't expected the Halls of Mandos to look exactly like his dingy quarters in Ered Luin.

Both are struck with a constricting sense of loss and an expanding sense of dread.