Place achiote paste, orange juice, lime juice, garlic, salt, oregano, cumin, and black pepper in a blender. Blend until smooth.
Place pork in a large bowl or resealable bag. Pour the marinade over the pork and toss until evenly coated. Cover and refrigerate for at least 12 hours or up to 24 hours.
Preheat the oven to 300°F.
Briefly pass the banana leaves over an open flame or rinse with hot water to make them pliable. Line a large Dutch oven with the banana leaves, allowing them to hang over the sides.
Transfer the marinated pork and all of the marinade to the Dutch oven. Add the bay leaves. Fold the banana leaves over the pork to enclose it. Cover with the lid.
Bake for 5 to 6 hours, or until the pork is fork-tender and easily shreds. The meat should reach an internal temperature of approximately 200°F to 205°F.
Remove the Dutch oven from the oven and let stand for 15 minutes.
Discard the bay leaves. Shred meat with two forks and toss shredded meat in juices until evenly coated.
Serve the cochinita pibil with warm corn tortillas, pickled red onions, habanero salsa, lime wedges, and cilantro.