Add the onion, garlic, ketchup, bourbon, Worcestershire sauce, sorghum, soy sauce, apple cider vinegar, whole-grain mustard, lemon juice, bay leaf and 1/4 cup water to a medium saucepan over medium heat. Stir to combine and bring up to a simmer. Continue to cook until smooth and slightly reduced, 25 to 30 minutes. Remove from the heat and strain to remove the onion, garlic and bay leaf. Refrigerate until ready to serve or for up to 2 weeks.
Sorghum syrup is made from the sweet juice of the sorghum plant, a variety of cereal grass. It's popular in the south as a sweetener for baked goods. You can find it at natural food stores or specialty online retailers.