In a medium sized bowl, add warm water. Add the sugar, make sure it dissolves, add the yeast, and make sure it dissolves. Let stand for 10 minutes, until it is creamy in color and foamy.
Add salt, mayonnaise, milk, and 2 cups of the bread flour. Start adding flour 1 tbsp at a time, until the dough chases the spoon around the bowl. Turn dough onto floured surface, and knead for 6 to 8 minutes.
Place dough into a greased bowl. Cover with a damp dish towel, or plastic wrap, let rise in a warm area for 1 hour. Punch dough down, knead again for 2 minutes. Place in a greased 9 x 5 loaf pan. Let rise again for another 40 to 45 minutes. Bake for 35 minutes at 375 degrees.