Fry bacon meanwhile in a medium saucepan over medium heat until brown and crisp, about 10 minutes. Transfer to paper towels to drain.
Pour off all but 1 tbsp. fat from pan. Add flour and whisk over medium heat. Pour in milk 1/4 cup at a time, whisking well after each addition (it will be very thick at first) until incorporated and smooth. Add cheeses in 3 batches, whisking continually and making sure each batch is mostly melted before adding the next.
Drain pasta, then stir into cheese sauce (it will thicken upon standing). Divide pasta among individual ramekins or bowls and top with bacon and chives.