1 Jamie: Well, whether you’re really a vampire or not, we need to get back home and make more TV shows. Bust more myths.
2 Jamie: We can test you out when we get back to our studio and all our equipment.
3 Adam: Okay. Just book us on a red-eye flight.
3 Jamie: To avoid sunlight?
4 Adam: And with most passengers sleeping, it’ll be less obvious if any are... inexplicably exsanguinated.

I checked if there are red-eye flights from Europe to the USA, and discovered that although it is indeed possible for a flight to depart Europe after sunset, fly through the night, and arrive in the USA before dawn, flights like this are very rarely scheduled because they're inconvenient for airport operating times. Almost all Europe-US flights depart during daylight and arrive in the evening.

I guess they'll just have to shop around and maybe get a flight with a weird connection in Greenland or something.