The word bigot originally meant hypocrite. Etymologists suggest (without complete consensus) that as early as the 11th century, the inhabitants of what is now France were disparaging the hated Norman invaders as "bigots" for two main reasons: 1) Bigot was a widespread given name among Normans, so it was like calling Germans Fritzes. 2) Normans enjoyed the way Englishmen swore "by God," and the conquerors used the phrase so much that the Franks associated it with them. (Similarly, the ancient Greeks thought foreigners who did not speak their language sounded as if they were stammering, and called them bar-bar-ians.)
The Normans also adopted the local Catholicism, and gained a reputation, as converts often do, of being self-righteously pious. This is where the association with hypocrisy came in, since people who are always calling on God to witness their virtue or patriotism tend to lead the most despicable lives - conquering ("discovering," "settling," "colonizing," "relocating"), exploiting ("trading"), murdering ("cleansing") and enslaving ("converting," "subjugating," "employing") in the name of their personal deity.
With self-righteousness comes intolerance of different religions, cultures and races. And so, instead of just hypocrites, we now have bigots.
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Sources: The Oxford English Dictionary, The Banhart Dictionary of Etymology, Webster's Collegiate Dictionary, The Random House College Dictionary.