Can't see Flybe moving to Bournemouth anytime soon. Bournemouth does not have such good transport links and such a move would probably result in a fall in pax no's.
Rechristen BOH "Southampton West", get FlyBe and others to market connecting longhaul services from "SOU-W" and then ferry lots of FlyBe connecting long haul pax by bus to/from SOU-E/SOU-W - would still take less time than connecting via different terminals at LHR!
