In a small saucepan, melt butter over medium. Whisk in flour and cook until bubbling, about 20 seconds, then whisk in milk, mustard, and 1 tablespoon water. Cook, whisking, until mixture is thickened and smooth, 1 minute. Add spinach and cook, stirring, until spinach is wilted and coated, 1 to 2 minutes. Season with salt and pepper and spoon onto bottom half of English muffin.
In a small nonstick skillet, cook bacon over medium until crisp and golden brown at edge, about 3 minutes, flipping once. Place bacon on top of spinach mixture. Return pan to heat and add egg. Cook until white is set but yolk is still runny, 2 to 3 minutes. Season to taste with salt and pepper and place on top of bacon. Sandwich with muffin top and serve immediately.