Heat a grill to medium. Grill the bread for a minute or two on each side, so it crisps and chars slightly. (If you are grilling other foods at another heat level you can still add the bread¿the goal is just to crisp and char it a bit.)
While the bread crisps, combine the tomatoes, peppers, parsley and green onions. Season well with salt and pepper. Add the olive oil and vinegar and toss again.
Place the arugula on top of the tomato mixture. Crumble the bread on top, leaving most of it in large pieces. Toss very gently, taking care not to crush the bread.