Melt the butter in a small saucepan over medium heat. Add the flour and cook, whisking constantly, until lightly browned, about 1 minute. Slowly whisk in the beer until smooth. Whisk in the mustard, hot sauce and Worcestershire until smooth. Gradually add the cheese, alternating between the Cheddar and the Stilton, a handful at a time, whisking until smooth and creamy before adding more, 3 or 4 minutes. Season with salt and pepper. Set aside.
Preheat the broiler. Arrange the bread in a single layer, brush with oil and lightly toast. Rub the oiled side of the toasts with the cut side of the garlic. Arrange tomato slices on the toasts, top with a layer of the cheese mixture and broil until the cheese is bubbly and just starting to brown, 2 or 3 minutes. Garnish with bacon, diced tomatoes and chives before serving.