I have found one place that has a Great White Shark experience. They do take you out free diving off the Farallon Islands in Isla Guada Lupe.
This is a link where you can read about the experinece: http://www.greatwhiteadventures.com/ This link has other shark diving information that is available.
They are now accepting reservations for 2013, since the 2012 season.
You can reach them with these phone numbers:
Great White Adventures
1-(888)-255-1528 (TOLL FREE)(NNN) NNN-NNNN- local
I do suggest if you book a trip like this you do take out trip insurace to protect yourself in case something comes up to postpone your trip.
Please let me know if I can be of further help.