Add all dry rub ingredients in jar with lid. Screw on lid; shake to evenly combine. Spread dry rub on both sides of rib pieces. Securely wrap in aluminum foil. Refrigerate for several hours.
Combine the onion, garlic, and bourbon in a 10-inch skillet over medium heat. Simmer for 10 minutes, or until onion begins to soften. Mix in the salt, pepper, chili sauce, tomato paste, vinegar, Worcestershire sauce, brown sugar, and hot pepper sauce. Bring to a boil. Reduce heat to medium-low, and simmer for 20 minutes. Allow to cool for 15 minutes. Purée in blender until smooth. If too thick, add water to desired consistency. Yield: About 2 cups.
*Note: There is enough Bourbon Infused Grilling Sauce to grill two racks of ribs.