Cook and stir bacon in a stockpot over medium heat until slightly browned, 5 to 10 minutes. Add onion, jalapeno pepper, and garlic; cook until bacon is slightly crisp, 5 to 10 more minutes. Add black-eyed peas, water, tomatoes, and beef bouillon; bring to a low boil.
Reduce heat and simmer, stirring frequently, until flavors have blended, about 30 minutes. Add Cheddar cheese and continue to cook, stirring frequently, until cheese is melted, about 15 minutes.