Prepare all the vegetables and the dressing up to a day ahead of time, and store them in separate containers. When you arrive at your destination, just toss them together, and serve.
Heat broiler. Place bell peppers, cut-side down, in a single layer on a baking pan. Broil until the skins start to blister, 6 to 8 minutes. Transfer the peppers to a medium bowl, cover with plastic wrap, and let steam. When cool enough to handle, remove skin and seeds. Chop flesh into 1/2-inch dice; set aside.
Place beet in a small saucepan; add cold water to cover, and bring to a boil. Reduce heat, and simmer until beet is tender when pierced with a knife, about 40 minutes. Drain. When cool, peel beet, and cut into 1/2-inch pieces; set aside.
Meanwhile, bring another medium saucepan of water to a boil. Fill a large bowl with ice and water, and set aside. Add green beans to the boiling water, and cook until bright green and just tender, 4 to 5 minutes. Drain, and plunge beans into the ice bath to stop cooking. When cool, trim ends, and cut beans into 1-inch lengths; set aside.
In a medium bowl, whisk together vinegar, lemon juice, sugar, salt, pepper, and mustard. Whisk in olive oil until mixture has emulsified. Whisk in 3 ounces blue cheese, and set aside. (You should have about 1/2 cup dressing.)
To serve, combine the reserved roasted peppers, cooked beet and green beans, lettuces, onion, celery, and the remaining 4 ounces blue cheese in a large bowl; toss. Drizzle with dressing, and toss again.