Scrape and thinly slice carrots; finely chop celery, onion, and green bell pepper.
Melt butter in a 3-quart saucepan over medium-high heat; add vegetables and garlic, and cook, stirring constantly, 5 to 7 minutes or until tender.
Add flour; cook, stirring constantly, 1 minute. Stir in chicken broth and milk; cook 5 minutes or until mixture is slightly thickened and bubbly.
Add shredded cheese, salt, and pepper, stirring until well blended. Stir in additional milk, if necessary, to reach desired consistency. Sprinkle with crumbled bacon.