Heat the olive oil in a large skillet over medium-high heat. Add the tofu slices in a single layer, and fry for 3-5 minutes on each side or until lightly golden.
Transfer the tofu to a plate lined with paper towels and cool slightly.
Spoon some barbecue sauce into the bottom of a container, preferably large enough to arrange the tofu in a single layer. Place the tofu pieces into the container, and spread the remaining barbecue sauce over the top.
Set aside to marinate for at least one hour, and up to overnight.
When you're ready to grill, heat the barbecue to medium-high. Place the tofu slices on the grill and brush with any barbecue sauce from the bottom of the container.
After 3-5 minutes flip the tofu, and brush the other side with extra barbecue sauce.
Grill for another 3-5 minutes until there are grill marks on the tofu. Remove onto a waiting plate.
For the barbecue tofu bowls
Divide the rice, greens, avocado, and tomato between 4 bowls.
Chop the tofu into cubes and distribute evenly between the bowls.