Bring a large pot of water to a boil over high heat and salt it. Add the pasta and cook until tender but not mushy, 8 to 10 minutes; drain and set aside.
While the pasta is cooking, place the bacon in a large skillet over medium-high heat. Once the bacon begins to color, add the onion and celery and cook until just soft, then add the chard and cook until the bacon is done. Add stock and beans, and sprinkle with salt and pepper; cook until heated through, about 5 more minutes. If it seems dry, add a little more stock or water; it should be moist but not soupy.
Add the pasta to the bean mixture and stir gently. Taste and adjust the seasoning, sprinkle with Parmesan.