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You need only two bridges total. One going from the top card to the middle card, and on the second connection of the middle card you have a crossfire bridge going to the third card.... a little dark but I think you will get the idea http://img17.imageshack.us/img17/620/20110822195836.jpg
Already been explained well, plus picture...
Already been explained well, plus picture, but I'll try to rephrase anyway just in case -- you (OP) were right when you said card 1 to card 2, card 2 to card 3. You don't need a special "tri-fire" bridge like you might use with Nvidia cards for three way SLI, because there is no dedicated connection between cards 1 and 3 needed for CrossfireX with 3 cards.