Heat a 12-inch skillet over medium-high heat. Cook the bacon, stirring often, until crisp, about 5 minutes. With a slotted spoon, transfer to a paper-towel-lined plate to drain, leaving the bacon fat in the skillet.
Cook the asparagus in the skillet with the bacon fat, stirring often, until crisp-tender and browned in spots, about 3 minutes. Season with 1/4 tsp. salt and, using a slotted spoon, transfer to the plate with the bacon. Add the vinegar, olive oil, mustard, 1/2 tsp. salt, and a scant 1/4 tsp. pepper to the fat in the skillet and whisk until combined.
In a large bowl, combine the asparagus, bacon, arugula, and almonds and toss with just enough warm vinaigrette to wilt the arugula. Serve immediately.