Place warm water into large bowl. Sprinkle in yeast; stir until dissolved. Add warm milk, sugar, salt, butter and 2 cups flour. Beat 2 minutes at medium speed of electric mixer, scraping bowl occasionally. Add 1 cup flour; beat 2 minutes at high speed. Stir in cheese, bacon, onion and enough remaining flour to make a soft dough. Knead on lightly floured surface until smooth and elastic, about 8 to 10 minutes. Place in greased bowl. Cover and let rise in warm place until doubled in size, about 1 hour.
Divide dough in half. Divide each half into 30 smooth balls. Place 3 balls in each section of greased (2-1/2-inch) muffin cup. Cover; let rise until doubled in size, about 30 minutes.*Brush rolls lightly with oil. Bake at 400oF for 15 to 20 minutes or until done. Remove from cups; serve warm.
* If desired, cover muffin pans loosely with plastic wrap; refrigerate 2 to 24 hours. When ready to bake, remove from refrigerator. Uncover rolls carefully; let stand 10 minutes. Bake as directed.