Heat milk, water and butter until warm (100° to 110°F). Pour into large mixing bowl and add yeast. Stir and let rest for 5 minutes. Beat in eggs.
Combine flour, sugar, baking soda and salt. Add to liquid mixture and beat on medium speed for 2 minutes. Combine cheddar cheese, Asiago cheese, bacon and chives in a bowl. Reserve one third, stir remaining cheese mixture into batter. Pour into greased 9-inch round cake pan. Cover and let rise until doubled, 40 to 50 minutes.
Bake in preheated 375°F oven for 20 minutes. Sprinkle remaining cheese mixture over bread. Return to oven and bake additional 5 to 10 minutes until well browned and bread is done. Cut into slices and serve warm. Refrigerate leftover bread.