Heat the oil in a small saute pan over medium heat. Saute the bacon strips until golden and crispy. Remove the bacon with a slotted spoon to a paper towel to drain and reserve. Pour off the oil and bacon fat, and reserve. Return the pan to the heat and add the vinegar and stir with a wooden spoon, scraping up any browned bits from the bottom of the pan. Whisk in about 4 teaspoons of the reserved pan drippings to make a dressing. Season with salt and pepper to taste and set aside.
Fill a small sauce pan with 3 inches of water. Add the distilled vinegar. Bring to a gentle simmer over medium heat, adjust heat to so the water is just under a simmer. Break the egg(s) into the water and poach to desired doneness, about 3 to 5 minutes.
Meanwhile toss the salad with the reserved bacon and the dressing. Season with salt and pepper.
Put the salad on a plate and place the toasts on the salad. Remove eggs from the water with a slotted spoon and pat the back of the spoon with paper towels. Place egg on toast and serve immediately.