Or you can take the train from Fareham, which takes 6mins, and walk from the train station via Rookery Avenue to the CTC, should take less than half an hour and there are trains that get into Swanwick for 07:42 so plenty of time!
As for the buses, they've obviously changed it since I last looked; in 2010 they had some that got to Whiteley for about 7:45. Is there not a NATS bus service from Swanwick to CTC?