In a large skillet over medium-high heat, heat oil. Cook bell pepper, stirring occasionally, until softened, 10 to 15 minutes.
Add ketchup and cook, stirring occasionally, until color has darkened, and ketchup is reduced to a thick paste, 7 to 10 minutes.
Add garlic and chili powder and cook, stirring, until fragrant, about 1 minute. Add vinegar, mustard, brown sugar, and Worcestershire sauce, season with salt and pepper. Cook, stirring frequently, until incorporated, for about 1 minute more.
Increase heat to high and add ground beef. Using a fork, break apart beef until separated and no big lumps remain. Cook, stirring frequently, until browned, for about 5 minutes.
Add tomato sauce and bring to a boil, stirring to combine. Let cool slightly; season with salt, if needed.