Heat cider, broth, Worcestershire, and garlic in a medium pot over medium heat and simmer for 5 minutes.
Toss the cheeses together in a medium bowl. Sift the corn starch over the cheese, and toss to coat lightly.
Using a wooden spoon, sprinkle some cheese mixture into the warm liquid and continue to stir in small amounts of cheese until it is all incorporated and the fondue is smooth and melted, about 15 minutes. Stir in cayenne, salt and Bourbon, if using.
Transfer to a fondue pot or double boiler and serve with desired dippers.
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