Combine syrup, rum, and bitters in highball filled with ice, top off with ginger beer. Squeeze lime wedge into drink, drop spent wedge into glass. Stir and serve.
For syrup: 1 cup sugar, 1 cup water, zest of two limes, 6-inch knob of ginger peeled and sliced thin. Combine ingredients in a medium saucepan, bring to low boil and remove from heat; let cool, strain and refrigerate up to one month.