In a heavy nonstick skillet, render bacon over medium heat until brown and lightly crisped; remove and keep warm. Pour off and reserve most of the bacon fat, leaving about a tablespoon in the pan.
Lightly season fish with salt and pepper. Cut any large pieces into bite-sized portions. Increase the heat to medium high and quickly saute the pieces in the bacon fat, turning once, until each is just cooked through (thin trimmings will take only a few seconds). Remove fish and keep warm with bacon.
Reduce heat to low and add 1 tablespoon of bacon fat to skillet. Saute shallot 30 seconds, then add honey, mustard, vinegar, and vegetable oil. Whisk together 1 minute, then remove from heat.
In a large bowl, toss greens with enough of the warm dressing to coat; adjust the seasoning with salt and pepper if necessary. Portion the salad onto individual plates and arrange the pieces of fish over it. Garnish with bacon.