Rub the inside of a medium saucepan with the garlic clove; discard.
Add the wine, lemon juice, and mustard and whisk. Heat to simmering over medium heat. Add the cheese, 1 cup at a time, and stir with a wooden spoon until smooth.
Pour into a fondue pot, or set the saucepan on a trivet. Serve immediately with the bread and potatoes.