I routinely make two to four hour transfers when I'm not doing 911. If the patient wants to rest, I let them, but my real life personality is blessedly pretty good, and I usually end up chatting with most of my patients. I've had some of the best conversations on long trips with patients I don't even know. I usually explain my background and inquire as to theirs (Old people have some of THE BEST stories!) and talk about my hobbies, unusual stories, and other things.
As for how to do it, the best thing I can think of is to not be...well, shy. Sometimes I start out asking something boring or stupid, and I usually promptly say, "Wow, that was boring or stupid." How are you around your friends? I treat everyone as a potential friend (Not psych pts, actually.) and I've never had a bad experience. Sure, some crazy whackos that might make me uncomfortable, but I roll with the punches and think of them as one of my crazy uncles. Works every time.
Anyway, it's personality. I personally need my alone time, and I can't stand having more than a few close friends. I still make sure that my patients receive the care and comfort they deserve, so making them comfortable with me as a person is included in the package.
Oh, and avoid being sunshine-sing-along-happy-friendly. While technically nice, it's not very real.