Fill large pot with water. Add 1/2 diced green pepper, two garlic cloves, beans and bay leaf. Bring to boil over high heat. Reduce heat, cover and simmer until beans are tender, about 1 hour.
In skillet over medium-high heat, warm olive oil. Add bacon; cook, turning, until bacon starts to brown, about 2 minutes. Add remaining green pepper and onion; cook, stirring, until slightly softened, about 3 minutes.
Chop remaining garlic cloves. Add to skillet with oregano, cumin and black pepper. Stir 1 minute. Pour in vinegar, scraping browned bits from bottom of pan with wooden spoon.
When beans are cooked, discard bay leaf. Transfer 1 cup beans to blender; blend to make paste. Return blended beans to large pot. Add bacon mixture and sugar. Stir well; bring to boil over medium heat. Lower heat, simmer and cook, uncovered, 20 minutes, skimming foam from top.