Preheat grill or broiler. In small bowl, whisk together olive oil, balsamic vinegar, salt, and pepper. Brush mushrooms, asparagus, and bell pepper with oil mixture.
Grill or broil vegetables 4 inches from heat, turning over once, until tender, about 10 minutes for asparagus and bell pepper, and about 12 minutes for mushrooms. When cool enough to handle, peel and slice pepper.
Turn off grill or broiler. Place bread on grill or broiler rack until warm, about 2 minutes.
Spread goat cheese on bread. Place mushrooms on each slice. Top with bell pepper and asparagus. Serve warm.