In small bowl, combine mayonnaise, sour cream and 1 packet Grilled Veggie Dip Mix. Mix until well combined. Cover and refrigerate 2 hours or until ready to serve.
In another small bowl, combine oil, vinegar and remaining packet Grilled Veggie Dip Mix. Divide vegetables between 2 (1-gallon) freezer bags. Pour oil mixture evenly over vegetables in both bags. Seal well and toss to coat. Let stand 10-15 minutes or up to 2 hours in refrigerator.
Prepare grill to medium heat. Place vegetables on grill and green beans in grill basket. Grill, turning occasionally, until crisp-tender or desired doneness, about 6-8 minutes.
Remove from grill. Slice peppers and mushrooms into strips. Let vegetables cool to room temperature. Place on a serving platter with dip.
Makes 12 servings.
Make Ahead: Prepare step 1 and 2 up to 1 day ahead. Refrigerate until ready to grill. Continue with step 3.