Hi, I hope I'm not too late. The site below seems to have all the train times, and it came up with "Lodon Waterloo" so I suppose you should go there. There's a train for Bournemouth approximately every 15 or 30 minutes (e.g. 12:30, 13:00, 13:15). It must be Firday the thirteenth syndrome!
www.thetrainline.com
is an excellent site for all information on train times, it plans journeys, gives prices and is adjusted with news about engineering works and so forth. You can book the tickets on it too.