Tear greens into large pieces and put in a large salad bowl with arugula, scallions, and chives.
Cook bacon in a 12-inch nonreactive skillet over medium heat until crisp.
Transfer bacon to paper towels to drain, then stir vinegar, sugars, salt, and 1/2 teaspoon pepper into fat in skillet. Boil, stirring occasionally, until reduced to about 3/4 cup, 10 to 12 minutes. (Dressing should be syrupy and bubbling.)
Crumble bacon over salad, then toss with enough warm dressing to lightly coat. Season with salt and pepper.
The vinegar, sugars, and seasoning (without bacon fat) can be boiled to reduce (by half) 2 days ahead.
Add to hot bacon fat, then bring to a boil just before making salad.