There're a few methods to counteract bitterness in mulled wine. 1. One way is to add a sweetener, such as honey or sugar. 2. The second way is to add an acidic ingredient, such as citrus juice or vinegar, and citrus fruits, such as oranges or lemons. 3. Thirdly, you can add spices, such as cinnamon or nutmeg to help balance out the bitterness. 4. Some people also find that adding a small amount of spirit, such as brandy, rum, or whisky, helps to round out the flavors. When it comes to choosing wine for mulling, opt for a full-bodied red wine with plenty of flavors.  Some good options include cabernet sauvignon, merlot, or syrah. If you're using white wine, look for a varietal with some sweetness, such as riesling or gewürztraminer.