Re: Flights
If you are flexible about your times and book them far enough in advance, I noticed that BA can be as little as £2 plus tax each way. I think FlyBe's lowest is £7 plus tax.
Should be no problem to book them a long way in advance if you know the college schedule.
Bournemouth Airport - Southampton by car: 40 mins, but allow an hour to include car parking. Last check in usually 30 mins before dep, but you can check in online with BA within 12 hours of departure if you buy a ticket online. Don't know about FlyBe
Long Term parking minimum charge £24. For stays of up to 24 hours, Short Term is better: £14.
Train from Christchurch-Southampton Airport might be more cost-effective but will take longer. Taxi Bournemouth-Southampton about £60 each way!!