In a large pot of boiling salted water, cook pasta, stirring occasionally and adding peas during the last minute of cooking, until al dente according to package directions. Drain pasta and peas and let cool.
Meanwhile, in a medium bowl, combine mayonnaise, mustard, vinegar, and cayenne; season with salt and black pepper.
Transfer pasta and peas to a large bowl. Pour dressing over and add bacon, cheese, and chives. Toss to combine; season with salt and black pepper, if needed. Serve immediately or refrigerate until ready to serve.
