Add the dry navy beans, 8 cups water, and salt to your Instant Pot. Seal the lid and cook on high pressure for 25 minutes. Once the timer beeps, allow the pressure to release naturally for about 10 minutes before manually venting any remaining pressure. Drain and rinse the beans thoroughly under cold water—this removes excess starch and gives you a cleaner final texture.
Clean and grease the Instant Pot, then set it to sauté mode. Add the bacon pieces and cook until crisp, about 5-7 minutes, stirring occasionally. Pour off most of the bacon grease, leaving about 2 tablespoons for flavor. Add the diced onion and red bell pepper to the pot and sauté for 3-4 minutes until softened and fragrant. I like to keep a bit of the bacon fat in the pot because it adds incredible depth to the final dish—don't drain it completely!
Turn off the sauté function and stir in the barbecue sauce, ketchup, spicy brown mustard, apple cider vinegar, and liquid smoke until well combined. Add the brown sugar and 1/2 cup water, then gently fold in the cooked beans from Step 1. Mix everything thoroughly to ensure the beans are evenly coated with the sauce and all the sugar has dissolved. The sauce should look glossy and well-combined at this point.
Sprinkle the smoked paprika and garlic powder over the bean mixture and stir to distribute evenly. Seal the lid and pressure cook on high for 15 minutes. Allow the pressure to release naturally for about 5 minutes, then manually vent any remaining pressure. I like to let the pressure come down gently because it helps the beans absorb the flavors without becoming mushy.
Open the lid carefully and give the beans a good stir. The mixture should have thickened and the flavors should have melded beautifully. If you prefer a thicker consistency, you can use the sauté function for a few minutes to reduce the liquid further. Taste and adjust seasonings if needed, then serve hot. These beans are delicious on their own or as a side to grilled meats.