In the second Bourne film (the first one directed by Greenglass), he starts off in Goa, then shows up in an airport in Italy, and later appears (with no indication of how he travels) in Munich, Berlin, Moscow, and New York City.
And, honestly, there wasn't a whole lot of visible "travel" in the "old" Bond, either. Bond is an agent of MI6, often with a cover as some kind of rich businessman or playboy. So of course he travels everywhere by passenger plane. (Unless he's doing some covert infiltration by parachute or surfboard or whatever.) The difference between Bond and (later) Bourne in terms of travel is that Bond has the resources of a wealthy government, while Bourne has... some kind of ninja superpower, I guess. In both cases, they mostly just translate invisibly from place to place.