To be honest, and this is merely my opinion - I think the only two "big" players would have to be Ryanair and Easyjet. The charters could, but they would only be seasonal. If they want an all-year carrier, then I would say FR or EZY.
If they both went to popular destinations, and with a strategic marketing plan; I don't see any reason why people would not use Bournemouth! I only go to STN because the flights are a) cheaper and b) not offered in BOH.
I wonder will SOU expand or renovate? This would have a huge impact into Bournemouth if they did! Just a thought...