Brush tuna fillets with olive oil; sprinkle with salt and pepper.
Grill, without grill lid, over medium heat (300° to 350°) 10 to 12 minutes or until fish flakes with a fork, turning once.
Cut bread on the diagonal into 8 3/4-inch slices, reserving remaining bread for other uses. Coat slices with cooking spray. Grill or toast each side until golden.
Spread Basil Mayonnaise evenly on one side of each bread slice. Layer 4 bread slices with tuna, lettuce, tomato, and bacon; top with remaining bread slices.