And since your first thought about me ran to 'orphan', that's what I'd say you are.' ― Vesper Lynd to James Bond

Which means you were at that school by the grace of someone else's charity: hence that chip on your shoulder. But you wear it with such disdain, my guess is you didn't come from money, and your school friends never let you forget it. Naturally you think human beings dress like that. by the cut of your suit, you went to Oxford or wherever. It's also possible (although unlikely) that Bond took a connecting flight.' All right. It's also possible that the 'last plane to Miami' didn't leave for a few hours and there were a few flights that left before that (Bond wouldn't have been able to follow Dimitrios until the last flight). He might have even gotten a coach seat deliberately to avoid running into Dimitrios. Since Bond secured a seat on the flight at the last minute, he may have had to get a coach seat against his will. If this flight was a small aircraft, it might not even have a first class (a Delta CRJ200, for example, does not have a formal first class area - just 'economy comfort' seats and JetBlue doesn't have first class on any of its flights). There are several possible explanations for this.

Regardless, it's extremely unlikely Dimitrios would not have spotted Bond - who had just robbed him of his beloved Aston Martin DB5 only hours earlier. It would be a relatively small aircraft flying the short distance from the Bahamas to Miami and let's face facts, both Bond and Dimitrios would probably be flying first class.

Bond then unceremoniously dumps her, leaves the beach condo and catches the same flight. While Bond is pumping Solange for information, she receives a phone call from Alex Dimitrios saying he will be on the last flight from Nassau to Miami.

Casino royale ending scene