Preheat oven to 450°F with rack in middle.

Sprinkle rosemary over bacon in a 4-sided sheet pan. Roast, turning once, until bacon is golden, 12 to 14 minutes. Drain on paper towels.

Meanwhile, bring water, milk, butter, a rounded 1/4 teaspoon salt, and 1/8 teaspoon pepper to a simmer in a heavy medium saucepan. Add grits in a slow stream, whisking constantly. Simmer over medium-low heat, covered, stirring often, until grits are tender and creamy, 10 to 12 minutes. Remove from heat and stir in cheese. Serve grits with bacon.