Preheat the barbecue to medium-high. Brush the pita bread with the oil. Grill on one side until nicely coloured, about 30 seconds to 1 minute. Remove the pita bread and set, grilled side up, on a large baking sheet. Turn the heat on the barbecue to low. Spread the pizza sauce on top of the pita bread; sprinkle with cheese and top with the bell pepper and pepperoni. Carefully set the pizza back on the grill; close the lid and cook 4 to 5 minutes, or until the cheese melted. Serve immediately.
Note: Greek-style pita bread is available in the deli department. Pizza sauce is available in the aisle canned tomato products are sold.