Add dried beans and 6 cups of water to Instant Pot and cook for 20 minutes on manual (high pressure) then allow pressure to naturally release. Drain beans then set aside.
Set Instant Pot to saute and add allow to preheat then add bacon and cook for 4-5 minutes until crispy. Add the chopped onion and pepper and cook for 2-3 minutes, stirring occasionally, until the vegetables are softened. Add the garlic and cook another 30-45 seconds. Set the Instant Pot to OFF. Add the tomato paste and cook for 1 minute stirring frequently.
Stir in the remaining 1 cup of water and scrape up any brown bits from the bottom of the pot. Add the barbecue sauce, ketchup, brown sugar, molasses, and dried mustard. Optional: You can add in 2 teaspoons of BBQ dry rub for extra flavor. Stir until well combined then add the reserved beans back to the pot.
Cover and seal the Instant Pot lid, then cook for 15 minutes on manual (high pressure). Allow pressure to naturally release until the pin drops. Remove the lid and stir the beans, then let cool for 5-10 minutes before serving.