Preheat the barbecue or indoor grill to medium-high. Brush the turkey with oil; season with cumin, chili powder, salt and pepper. Grill, lightly oiling the surface if prone to sticking, 3 to 4 minutes per side, or until cooked through. Lower the heat.
Top the turkey with cheese and bacon and cook until the cheese melts. Spread the buns with mayonnaise. Top bottom buns with lettuce and tomatoes. Top with turkey, top buns, and serve.