Prepare and bake cornbread according to package directions; set aside to cool.
Crumble cornbread into a large serving bowl. Add beans, corn, onion, tomatoes, celery, 1/4 cup bacon bits and 1 1/2 cups cheese. Toss well; set aside.
In another bowl, mix sour cream and salad dressing together; drizzle over cornbread mixture and toss to coat. Sprinkle with remaining bacon bits and cheese.