Prepare barbecue (medium-high heat). Whisk together black bean sauce, garlic, soy sauce, sesame oil, lime juice, and ginger in shallow dish. Set 2 tablespoons marinade aside. Add pork to remaining marinade; let stand 20 minutes.
Remove pork from marinade; brush cut side of bok choy with reserved 2 tablespoons marinade. Grill pork until just cooked through and thermometer inserted into thickest part registers 145°F, about 5 minutes per side. Grill bok choy until softened and lightly charred, about 5 minutes total.
Divide pork and bok choy among 4 plates. Sprinkle with cilantro, garnish with lime wedges, and serve.