Slice the persimmons into rounds a little less than ¼ inch thick, then cut the rounds in half to form semicircles. Count the pieces to determine how much bacon you'll need--each full slice of bacon is enough for two persimmon semicircles.
Preheat the oven to 375°F and line a baking sheet with foil for easy cleanup. Arrange the halved bacon slices on the sheet and bake for about 10 minutes, until starting to brown but still very bendy. Transfer the bacon to a plate lined with paper towels to drain and cool. Increase the oven temperature to 400°F.
Mix the goat cheese and rosemary in a small bowl. Top each persimmon slice with a teaspoonful of herbed goat cheese rolled into a ball. Wrap a piece of bacon around each one and secure it with a toothpick.
Place the persimmon bacon bites on a clean baking sheet lined with foil or parchment and roast for 15-20 minutes, or until the bacon is cooked through. Cool for at least 5 minutes and serve warm with chilled white wine.