Place warm water, salt, sugar, flour, and yeast in the bread machine pan in the order recommended by the manufacturer. Select Dough setting.
When cycle is complete, let dough rest on a lightly floured surface. Meanwhile, in a large pot, bring 3 quarts of water to a boil. Stir in 3 tablespoons of sugar.
Cut dough into 8 equal pieces, and roll each piece into a smooth ball. Flatten balls, and poke a hole in the center of each with your thumb. Twirl dough to enlarge hole, and to even out the dough around the hole.
Carefully transfer bagels to boiling water. Boil for 1 minute, turning halfway through. Remove with a slotted spoon, and drain briefly on a clean towel. Arrange boiled bagels on a baking sheet.
Bake in a preheated 375°F (190°C) oven for 20 to 25 minutes, until well browned.