Gatwick Airport to Bournemouth Airport would probably take you about 2 and a half hours in clear traffic. Unless you plan to leave very early in the morning, I would strongly advise against driving to Bournemouth from London first thing. The traffic will be terrible on the motorways and it doesn't look good if you walk in late. Remember you're supposed to be there for 8:45am.
I recommend you do what a lot of people do - drive down to Christchurch the night before, stay in a Guest House (cheap, very comfortable and the breakfasts are VERY good!) and then drive up to Bournemouth Airport (about 15 minutes drive) in the morning. As well as eliminating the risk of getting stuck in traffic on the motorway, you'll have the added benefit of a good night's sleep which is essential before Phase 2. The computer PILAPT tests require all the concentration you can summon up. You're unlikely to be at your best if you have to get up at 6:00am and then drive over two hours in heavy motorway traffic.
Also, you can get the train from Gatwick Airport down to Christchurch (with one change) and use taxis to get to Bournemouth Airport if that's cheaper than hiring a car for two days.
About the question "has anyone undergone phase 2" - please read through this thread very carefully, particularly the most recent 10-15 pages or so. That question has been asked repeatedly and there is a large amount of useful information on here - all I would be doing by answering this would be repeating what has already been posted.
Best of luck
