Setting up an airline at Bournemouth would be near impossible for the following reasons:
1. The airport would need to offer all airlines a similar airport deal - so no protection from Ryanair or others.
2. It would be very difficult if not impossible to achieve the economies of scale you would need to make a new airline profitable. Profitability only comes with size, scale and growth - Bournemouth is limited and the UK is saturated.
3. You would need a large aircraft to get the cost per seat low enough to compete with Southampton. If not your demand pool will be tiny and therefore unviable. In my mind Embraer or C series or MRJ is the right aircraft but they are very expensive to lease/purchase
BOH's best bet is to attract easyJet or overflow flybe routes from SOU.