This is a simple combination of ingredients that I find refreshing. When I was growing up, my father would always serve a huge salad and say "You always need a few leaves to feel good". It is his salads that I carried with me throughout my career as a chef and mother.
In a large skillet, over medium heat, add the bacon and 1/2 cup water. Bring the water to a boil and reduce until it evaporates. The bacon will start to render its fat and brown. Lower the heat and allow to cook at a slow, steady pace. When the bacon is crispy and light brown, drain the fat into a medium-size bowl and set the bacon aside. Put the shallots on a flat surface and cut them into thin rounds. Transfer to a large salad bowl and season them with salt, to taste. Add the red wine vinegar and mustard and stir to blend. Stir in the bacon fat, tasting as you go. Start with about 1/4 cup of the fat and taste as you add the rest. There should be a good balance between the bacon flavor and the acidity of the red wine vinegar. Set aside. Put the radishes on a cutting board and, using a small, sharp knife, slice them into 1/4-inch rounds (with the bit of the tops still attached). Add them to a small bowl and stir in the mustard. Add the Bibb lettuce to the bowl with the bacon dressing. Toss to blend. Taste for seasoning, then stir in the radishes and the cooked bacon. Serve immediately.
For optimum results, chill the lettuce and radishes before tossing and serving. This salad is so refreshing when eaten cold!